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James McKirdy. 

LOGIC: 

James McKirdy. 
)EDIJCTIVE AND INDUCTIVE. 



BY 

ALEXANDER BAIN, LL. D., 

ROFE8SOR OF LOGIC IN THE UNIVERSITY OF ABERDEEN. 



NEW AND REVISED EDITION. 



NEW YORK: 
D. APPLETON AND COMPANY, 

I, 3, and 5 BOND STREET. 

1887. 



# 



Gfft from 
Wr. James McKirdy 

Jan. 19,193a 



PREFACE. 



The present work aims at embracing a full course of Logic, 
both Formal and Inductive. 

In an introductory chapter, are set forth such doctrines 
of psychology as have a bearing on Logic, the nature of 
knowledge in general, and the classification of the sciences ; 
the intention being to avoid doctrinal digressions in the 
course of the work. Although preparatory to the under- 
standing of what follows, this chapter may be passed over 
lightly on a first perusal of the work. 

The part on Deduction contains the usual doctrines of 
the Syllogism, with the additions of Hamilton, and a full 
abstract of the novel and elaborate schemes of De Morgan 
and Boole. 

The Inductive portion comprises the methods of induc- 
tive research, and all those collateral topics brought for- 
ward by Mr. Mill, as part of the problem of Induction ; 
various modifications being made in the manner of state- 
ment, the order of topics, and the proportion of the hand- 
ling. The greatest innovation is the rendering of Cause 
by the new doctrine called the Conservation, Persistence, 
or Correlation of Force. 

Mr. Mill's view of the relation of Deduction and Induc- 
tion is fully adopted, as being the solution of the otherwise 
inextricable puzzle of the syllogism, and the means of 
giving unity and comprehensiveness to Logic. 



Jv PREFACE. 

rate division is appropriated to the Logic of the 
, with the view of still further exemplifying the 
;il methods, and of throwing light upon various points 
in the sciences themselves. The review comprises all the 
Tetical or fundamental sciences — Mathematics, Physics, 
iiistry, Biology, and Psychology ; the sciences of Classi- 
ion, or Natural History; and two leading Practical 
—Politics and Medicine. 
The department of Definition is, for the first time, 
■;ht under a methodical scheme, and rendered of co- 
ordinate value with Deduction and Induction, as a branch 
g ical method. The modes of defining, as a generalizing 
gfgfc are given under two canons, a positive and a 
live; and attention is called to the chief obstacles — 
uncertainty in the denotation of words, and the gradual 
transition of qualities into their opppsites. 

In discussing Fallacies, I have canvassed the grounds 

for the usual practice of detaching the violations of logical 

rules from the exposition of the rules themselves ; and 

endeavoured to show that the only portions of the 

subject proper to reserve for separate handling, are the 

Fallacious tendencies of the Mind, and Fallacies of Con- 

n. As these are subjects of great moment, and admit 

: .de illustration, both are considered with some minute- 

ne of the controversies in the subject are overlooked ; 
but it has been deemed advisable to separate them from 
the main body of the work. In an Appendix, are em- 
ad the various Classifications of the Sciences, the Pro- 
B of Logic, the Classification of Nameable Things, the 
ll Postulate, the meanings of Analysis and Syn- 
bl Theories of Induction, the Art of Discovery, 
and the maxims of Historical Evidence. 
To adapt the work to an elementary course of Logic, 



PREFACE. V 

the parts to be omitted are the Additions to the Syllogism, 
the Logic of the Sciences, and the chapters in the Appen- 
dix. The junior student, or the candidate for a pass 
examination, without attempting to master or commit these 
reserved portions, might yet find their perusal of service 
in understanding the rest. 

There is a general conviction that the utility of the 
purely Formal Logic is but small ; and that the rules of 
Induction should be exemplified even in the most limited 
course of logical discipline. I would suggest that an in- 
creased attention should be bestowed on Definition and 
Classification, with reference both to scientific study and 
to matters not ordinarily called scientific. 

As I may be open to the charge of presumption in 
appearing as a rival to Mr. Mill, I will venture the remark, 
that an attempt to carry out still more thoroughly the 
enlarged scheme of logical method, seems the one thing 
hitherto wanting to the success of his great work. 

Aberdeen, March, l&7d 



CONTENTS. 



Introduction 



"jWK 



BOOK L 

NAMES, NOTIONS, AND PROPOSITIONS. 

CM XT. 

I. Names or Terms ...... 42 

II. Classes, Notions, or Concepts . . . . 61 

IIL Propositions . ... 73 

BOOK IL 

DEDUCTION. 

I. The Syllogism . . . . . 1 33 

II. Recent Additions to the Syllogism . . . .178 

IIL Functions and Value of the Syllogism . ... 207 

IT. Trains of Reasoning and Deductive Sciences . . .214 

V. Demonstration — Axioms — Necessary Truth . . 219 

BOOK IIL 

INDUCTION. 

I. Meaning and Scope of Induction . . . 231 

IL The Ground of Induction — Uniformity of Nature — Laws of Na- 
ture ....... 238 

IIL Induction of Coexistence . . . . 241 

IV. Law of Causation . . . . . . 245 

V. Elimination of Cause and Effect — Observation and Experiment 271 
VL The Experimental Methods . . . . .279 

VII. Examples of the Methods ..... 297 

VIII. Frustration of the Methods . . . . .306 

IX Chance, and its Elimination . . . .314 

X. Induction aided by Deduction ..... 325 

XL Secondary Laws — Empirical and Derivative . . 332 

XIL Explanation of Nature ...... 346 

XIIL Hypotheses . . . . .358 

XIV. Approximate Generalizations and Probable Evidence . . 365 

XV. Analogv 370 

2CVL Credibility and Incredibility . . . . .378 



\ 111 



CONTENTS. 



BOOK IV. 

DEFINITION. 



pitr. 

i mods of Definition 
II. (i. noiai Names 
III Classification 



PAGB 

384 
401 
414 



BOOK V 




LOGIC OF THE SCIENCES. 




I. Logic of Mathematics .... 


. 429 


II. Logic of Physics ..... 


451 


III. Lo^ie of Chemistry .... 


. 472 


IV. Lo^ic of Biology ..... 


488 


V Logic of Psychology . . . . . 


. 505 


\ I. S .mes of Classification .... 


522 , 


VII. Logic of Practice 


. 545 


VIII. Logic of Politics ..... 


547 


IX. Logic of Medicine . . .. 


. 575 


BOOK VI 




FALLACIES. 





I. Mill's Classification of Fallacies 

II. The Position of Fallacies 

III. Fallacious Tendencies of the Mind 

IV. Fallacies of Confusion . 
V. Logical Fallacies 



599 
60S 
606 
616 
625 



APPENDIX. 

A. — Classifications of the Sciences 

B. — The Province of Logic 

< — Enumeration of Things . 

I' —The Universal Postulate 

E — Aristotelian and Scholastic Fallacies 

F— Analysis and Synthesis 

irowth of the Logic of Induction 
D. — Art of Discovery 
I. — Historical Evidence 
K— Explanation of Some Logical Terms 



627 
639 
652 
664 
673 
681 
687 
697 
707 
715 



PART I. 

DEDUCTION". 



INTRODUCTION. 



1. Logic may be briefly described as a body of doctrines 
and rules having reference to Truth. 

The functions of Logic will be afterwards given with par- 
ticularity and precision. For the present we remark that it 
concerns the Truth of things, no matter what the subject be. 
While in one aspect it is theoretical, in the prevailing aim it is 
practical. 

In this introductory chapter we are to consider the following 
topics. 

(1) The Psychological data or groundwork of Logic. 

(2) The First Principles of Logic. 

(3) The Classification of the Sciences. 

(4) The different views of the Province of Logic. 

(5) The Divisions of Logic. 

PSYCHOLOGICAL DATA OP LOGIC. 

2. Logic, under every view, involves frequent references 
to the laws and workings of the mind ; and the more so 
the more we extend its province. • 

In the common Logic of the Schools, the Syllogistic or 
Deductive Logic, explanations are usually given of the intel- 
lectual processes named Perception or Simple Apprehension, 
Abstraction or the formation of concepts or notions, Judgment 
or the laying* down of propositions, and Reasoning or the 
drawing of inferences or conclusions from premises. 

In the Inductive Logic, an enquiry is instituted into our 



2 PSYCHOLOGICAL DATA OF LOGIC. 

idea of Cause ; in connection with which, notice is taken of 
the controversy respecting the Origin of our Knowledge in 
the Mind, namely, as to whether it be wholly derived from 
experience, or whether any portion of it fas Cause, the Axioms 
of Mathematics, &c.) be intuitive, instinctive, or innate. 

It is considered a part of Logic to set forth the theory and 
the limits of the Explanation of phenomena ; for which pur- 
pose a reference must be made to the structure of the mental 
powers. This was the avowed aim of Locke, in his Essay on 
the Understanding, one of the greatest contributions to the 
science of mind. 

Under such circumstances, the most satisfactory course ap- 
pears to be to bring forward and expound, once for all, at the 
commencement, whatever portions of Psychology are in any 
way implicated with the rules aud methods of Logic. But the 
exposition must necessarily be brief. 

Discrimination or Relativity. 

3. In order to make us feel, there must be a change of 
impression ; whence all feeling is two-sided. This is the 
law of Discrimination or Eelativity. 

Observation shows that unbroken continuance of the same 
impression is attended with unconsciousness ; and that the 
greater the change or transition, the greater tho consciousness. 
An unvarying touch, or a monotonous sound ceases to be felt ; 
in an even temperature, we lose all consciousness of heat or 
cold. Still more convincing are the instances showing that 
changes affect us in proportion to their greatness and sudden- 
ness. Abrupt transitions are stimulating and exciting ; the 
first exposure to sun-light after being in the dark, the first 
mouthful of water when we are thirsty, the moment of transi- 
tion from poverty to wealth— are accompanied with the highest 
degree of feeling ; after which there is a gradual subsidence of 
the excitement. 

Hence the fact of our being under some agency of sense or 
feeling does not of itself attest our mode of feeling; there 
must farther be given the condition immediately, and for 
some time previous. That a man is the possessor of a thou- 
sand pounds to-day is not a sufficient criterion of his feel- 
ings as regards worldly abundance. If a year ago, the same 
man possessed nothing, he feels in a way totally different from 
him that has fallen to that amount from a fortune often thou- 
sand pounds. 






DISCRIMINATION OR RELATIVITY. 3 

4. As regards Knovjledge, there must likewise be a tran- 
sition, or change ; and the act of knowing includes always 
two things. 

When we consider our mental states as Knowledge, the 
same law holds. We know heat by a transition from cold ; 
light, by passing out of the dark ; np, by contrast to down. 
There is no such thing as an absolute knowledge of any one 
property ; we could not know * motion/ if we were debarred 
from knowing ■ rest.' No one could understand the meaning 
of a straight line, without being shown a line not straight, a 
bent or crooked line. 

We may attend more to one member of the couple than to 
the other. In this way only can we think of an individual 
property. We may be thinking more of the heat than of the 
cold, of the straight than of the crooked ; the one may be the 
explicit, the other the implicit subject of our thoughts. As our 
transitions may be in two directions— from heat to cold, and 
from cold to heat — we have a difference of feeling in the two 
cases. We are more conscious of heat, when passing to a 
higher temperature, and of cold when passing to a lower. The 
state we have passed to is our explicit consciousness, the state 
we have passed from is our implicit consciousness. 

The principle of Relativity has wide and important bearings 
in Logic. It will appear in Naming ; in Definition ; in Pro- 
positions or Affirmation. It will be appealed to in rectifying 
a large class of Fallacies — the fallacies of the suppressed rela- 
tive, or of the Absolute. 

Agreement or Similarity. 

5. When an impression is repeated, after an interval, we 
are affected with a new and peculiar consciousness, the 
shock or consciousness of Agreement in difference. 

We see a candle flame ; it is withdrawn ; after a time, it is 
brought back. We have now, in addition to the luminous 
effect of the presentation, a shock or feeling of agreement, 
identity, repetition ; a state no less concerned in our intellec- 
tual operations than the shock of difference or discrimination. 
We are constantly experiencing the repetition of former im- 
pressions, in circumstances more or less altered, and we are 
affected with a greater shock according to the greatness of 
the alteration. The degree or intensity of the consciousness 
of Agreement may vary through a wide range, from the slight 



4 PSYCHOLOGICAL DATA OF LOGIC. 

recognition of a new day to the flash of a great discovery of 
identification, like Newton's assimilating the fall of a stone to 
the deflection of the moon towards the earth. 

Knowledge as conjoining Difference and Agreement 

6. Our knowledge of a fact is the Discrimination of it 
from differing facts, and the Agreement or identification of 
it with agreeing facts. 

The only other element in knowledge is the Retentive 
power of the mind, or memory, which is implied in these 
two powers. 

Our knowledge of heat is (1) a series of shocks of Difference 
or discrimination between heat and cold, and (2) the Agree- 
ments or repetitions of the same shocks under change of 
circumstances. 

Besides the transition heat-cold, which is the primary cog- 
nition of heat, we make other transitions into other sensations. 
We have occasion to pass from a sensation of warmth to a 
sensation of light, and the difference of the two brings out a 
new discriminative consciousness, and gives a new meaning to 
warmth, and also to light ; heat is no longer simply the con- 
trast of cold, it is also the contrast of the feeling of luminosity. 
So, every new sensation that we pass to from heat, with con- 
sciousness of difference, gives a new negative meaning to heat ; 
it is not taste, nor smell, nor hardness, nor sound. 

Again, our mental impression, knowledge, or idea of a 
shilling, is the sum of all its differences from the things that 
we have contrasted it with, and of all its agreements with the 
things that we have compared it to. We call it round ; sig- 
nifying that it differs from things called square, oblong, oval, 
&c. ; that it agrees with other things called round — that we 
have been frequently struck with the identity of this figure in 
many different combinations. 

So with the weight of the shilling. We know weight by 
difference, and by agreement ; we recognise a shilling as heavier 
than some things, lighter than others ; which is difference ; and 
as identical with a third class, which is agreement. 

The knowledge, idea, or recollection of any concrete 
object, is thus the aggregate of those mental exercises of 
Discrimination and Agreement, fixed and retained in the 
mind by the power called retentiveness, or memory ; by which 
power of retention we are able to discriminate and compare 









VARIETIES OF KNOWLEDGE. - 5 

present impressions with past, and to accumulate a vast stock 
of mental effects or deposits, called ideas, knowledge, thought. 

Knowledge is of two hinds, called Object and Subject 

7. The knowledge of a shilling, of a house, of a mountain, of 
a star, is said to be objective ; it relates to the object, or the 
outer, world. The knowledge of a pleasure or a pain, or of 
the succession of ideas in the mind, relates to the subject, or 
the internal, world. We have a great accumulation of both 
kinds of knowledge ; some minds abounding more in one, some 
more in the other. 

Knowledge as (1) Individual and Concrete, or (2) General 

and Abstract 

8. The knowledge of a table in a room, at a particular time, is 
in the highest degree individual or concrete. The knowledge 
relating to any table, at any time, is said to be general and 
abstract. By the mental power of Agreement or Similarity, 
we bring to mind different individual tables, attending to their 
points of community, in spite of many diversities. We affirm 
properties common to them all. This is the generalising 
power of the mind. It is one of the most signal functions of 
our intelligence, and is purely an outgoing of the fundamental 
power named Agreement, or Similarity. 

Dispute as to the CJiaracter of General Knowledge, called 
also Abstract Ideas, 

9. In General Knowledge, strictly so called, there is 
nothing but the fact of agreement among a number, of 
separate particulars ; which agreement is signified by the 
use of a common name. 

A general name, as * circle,' * round/ ' animal,' * wise,' is 
applied to things agreeing in a certain respect, while differing 
in other respects, to signify their agreement. 

It has been supposed that the points of community of 
agreeing things exist apart from the things. This view is 
called Realism. 

It was believed by a certain school of philosophers, deriving 
from Plato, that there exists, in the universe of being, a Circle 
in general, or circular Form without substance, size, or colour ; 
that in like manner, there are archetypal Forms of Man, of 



6 PSYCHOLOGICAL DATA OF LOGIC. 

Just, of Good, &c. After a severe controversy, which raged 
in the scholastic period, this view was abandoned. 

Realism is still exemplified, however, in the doctrine of an 
Independent External World, and also in the doctrine of the 
separate existence of Mind or Soul. In strictness, the External 
World is known only as perceived by our senses; Mind is 
known only as conjoined with body. 

Another mode of regarding the fact of community in 
diversity, is to suppose that the mind can represent to it- 
self in a notion, the points of agreement by themselves, 
and can leave entirely out of sight the points of differ- 
ence. This is Conceptualism. 

Although there is no pure circle in existence, we are sup- 
posed able to think of the round figure to the exclusion of the 
other properties of the individual circles — material, colour, size. 

This too is incorrect. It exaggerates the mind's power of 
giving a preference of attention to some of the attributes of a 
concrete object, as a wheel, or a shilling. We may think 
much of the roundness, and little of the size ; but we cannot 
think of the roundness, without thinking of some size or 
colour. 

The usual mode of thinking an abstraction, or of concen- 
trating the mind upon one property, is to think alternately of 
the different objects possessing the property. We can best 
think of roundness, by having in view various round things, 
differing in material, size, colour, &c. The effect of the mind's 
passing and repassing between the individuals, is that the 
roundness starts into great prominence, and the other proper- 
ties fall into the background, without, however, being extin- 
guished. The great fact constantly underlying Abstraction, 
is the mustering of individuals agreeing in the midst of differ- 
ence. 

We are in the habit of using single individuals to typify a 
multitude ; as in the diagrams of Euclid. We do not, in 
geometrical reasoning, think of a great number of circular 
things ; we can study the circle upon one figure, provided we 
take care to affirm nothing as to size, colour, or material, 
which facts are inseparable even from the barest diagram. 

When the logician speaks of a Notion, Concept, or Abstract 
Idea, he must not be understood as implying anything be- 
yond the agreement of a certain number of things in a given 
manner. 



TflK INDIVIDUAL AND THE GENERAL. 7 

Our idea of an Individual a conflux of Generalities. 

10. What we term the Perception of an individual, as a 
given tree, is not simply a sense impression of the moment, 
it is an aggregation of many generalized impressions. 

When we look at a tree, we are affected by a great number 
of different influences — colours, shape, size, &c. Now, every 
distinguishable impression recalls the previous stamps of the 
same, by Agreement or Similarity ; and the idea of the tree is 
not an original sense presentation, but a compound of this 
with old presentations. Every feature of the tree suggests a 
classification upon that point ; the green and brown colours 
are felt only as the collective impressions of those shades of 
colour. 

In our minds, therefore, the Concrete and the Abstract are 
inextricably blended. Of a pure concrete, not also resolved 
into classifications or abstractions, we have no experience. 
Oar knowledge proceeds in both ways at once; individuals 
giving generals and generals re-acting upon individuals. If 
there was one concrete thing in the world, having no property 
in common with any other known concrete thing, we might, 
by gazing upon that, and comparing it with itself, possess an 
idea of a concrete individuality, where no generality was im- 
plicated ; but such a concrete would be very different from any 
concrete known to us. We are not in the position to imagine 
such an idea. 

11. The speciality of a concrete Individual is that it is a 
definite aggregate not confounded with other individuals. 

The number of general properties pointing to the individual 
must be such as to give it a definite or special character, 
instead of leaving it indefinite or common. The tree that I 
now look at, is individualized by a concurrence of properties 
never realized before ; or if not by such concurrence itself, by 
its surroundings, and all the circumstances of time and place, 
accompanying its perception. A shilling is individualized 
by its adjuncts of place and time. 

12. The distinction between Presentation and Represent- 
ation, is the distinction between a definite conflux of 
generalities, and an indefinite conflux. 

A shilling in the hand is a Presentation. A shilling as a 
general coin of the realm is Representative ; it is common to 



g PSYCHOLOGICAL DATA OF LOGIC. 

many places and times and circumstances, and not bound 
down to one definite situation and one definite moment. 

1 3. The names of Individuals usually correspond to their 
character as a conflux of generals. 

In a few instances, we have names that bear no reference to 
generalities, as when a certain individual man is named — Cassar. 
These are proper, or meaningless names ; the bare symbols 
for separating the thing from other things. But in the vasfc 
majority of instances, the name follows the manner of conceiv- 
ing the thing — that is, by specifying the concurring generalities. 
A large gothic building ; a stout man of forty ; a cubical 
crystal, with a certain hardness and specific gravity, found in 
a certain formation : — are examples of designations in strict 
accordance with the ideas of the things. 

Philology confirms this. The primitive names of such con- 
crete objects as sun, moon, father, mother, have all a gene- 
ralized meaning ; i moon ' is the measurer, * father ' is the 
feeder, and so on. There seems to be no possibility of con- 
ceiving individuals without classifying and generalizing at the 
same time ; and the one name means both an individual and 
a general. 

The intellectual function of Agreement, or Similarity, as the 
basis of Reasoning. 

14. Reasoning, in every form, supposes the operation of 
Similarity— the assimilating of one thing to some other 
thing. 

The most general type of Reasoning is to infer from one 
particular fact to another particular fact of the same kind • 
the likeness being both the means of suggestion, and the iusl 
tification of the transfer of properties. We throw a stone into 
a pool; it makes a splashing noise, sinks to the bottom, and 
oitfuses a series of waves from the point where it fell We 
infer or reason, or presume, that another stone thrown into 
the same pool will be followed by the same series of effects; 
and we may extend the inference to another pool, or to an^ 
mass of liquid. This is to infer, to reason, to transcend our 
actual experience to make an affirmation respecting the un- 

SSr to tak°e W th?^ f mind iS P rom P ted h J the likeness of the 
h^Ln n £ tep m advance > to anticipate what is to 

happen. One would not infer that a handful of dried leaves 



KINDS OF REASONING. 9 

would produce all the consequences of throwing the stone ; 
we never expect either through our instinctive belief, or 
through our experience of the world, that the same effects 
will arise under different circumstances. 

This mode of Reasoning is in constant use, and extends to the 
animal intelligence. An animal accustomed to find a shelter 
under a bush, reasons from one bush to another bush, being 
moved solely by the resemblance of the second to the first. A 
dog is deterred by the menacing movement of a strange per- 
son wielding a strange stick : the partial resemblance to 
former experiences is enough to rouse its fears. 

A second mode of Reasoning is when by the help of general 
language, we infer from one or a few cases, to all cases of the 
kind ; as when we conclude, after a certain number of trials, 
that all stones sink in water, that all matter of vegetable origin 
is combustible, that all animals are generated from other 
animals. This is Induction, in the more technical sense — the 
inferring not from particulars to other particulars, but from 
particulars to universals. The mental process is still Simi- 
larity, or the process whereby one thing suggests other 
resembling things. It is by similarity that we assemble in 
the mind all kindred facts that have ever come under our 
knowledge ; we then are able to compare the points of agree- 
ment, with a view to an accurate general statement, in other 
words, an Inductive proposition. 

The third kind of Reasoning, called Deductive, is also based 
on the tracing of resemblance. When we infer that, because 
all stones sink in water, a certain body will sink (which is 
Deduction), it is because that body resembles the rest, or has 
the points of community indicated by the general word 
* stone.' When we have mastered a general principle, it is 
by similarity that we discover cases to apply it to, and so ex- 
tend our knowledge deductively. 

Origin of our Knowledge in Experience. 

15. Our knowledge of the world, both of matter and of 
mind, is the result of our conscious Experience. 

As regards the Material, outer, or object world, we gain 
our knowledge through the ordinary Senses, coupled with 
our Movements, under the three laws of our Intelligence — 
viz., Difference, Agreement, and Retentiveness. We see, hear, 
touch, taste, smell ; we have our active energies aroused by 
things resisting, by movements, and by things extended ; we 



!Q PSYCHOLOGICAL DATA OF LOGIC. 

discriminate and identify impressions ; we acquire permanent 
reflections, and associate things presented in combination; 
and by all these processes (exemplified at full length m Mental 
Science, or Psychology) we lay up our stock of imagery, 
id**, or thoughts, of the world of sensible experience. 

As ro«rda the Mind, or the knowledge of our inner life 
the senses do not avail us. We are directly and immediately 
conscious of our feelings, thoughts, and volitions, and acquire 
a store of permanent recollections of these also. We remem- 
ber our different pleasures and pains, and the order of their 
occurrence ; we learn not merely things, but our ideas of 
thin<rs, and the laws of the rise and succession of these ideas. 
Thus, it is a fact of our mental or subjective life, that we 
easily recall to mind whatever strongly engaged our attention 
in the reality. 

16. It has been alleged that some parts of our knowledge, 
instead of being the result of experience, like the greater 
portion, are intuitive or inherent to the mind, apart from 
the operation of the senses upon actual things, or the par- 
ticular phenomena of the subjective consciousness. 

At different stages in the progress of Philosophy, there have 
been given different lists of intuitive, or a priori elements of 
knowledge. At the present day the controversy turns chiefly 
on these four notions — Time, Space, Substance, Cause. 

It is maintained that there is in these notions something 
that experience could not give ; so that some different origin 
must be sought for them. 

On the other side, the supporters of the Experience theory 
hold that the Moving energies, with the Senses and Self-Con- 
sciousness, aided by the intellectual functions, can account for 
all these notions. 

For example, Time is an abstraction : and, like all other 
abstractions, is, properly speaking, a certain mode of likeness 
among individual things or feelings of the mind. All our 
experiences, whether object or subject, are regarded by us as 
more or less enduring ; the attribute of Time is the assimilation 
or classification of enduring states, as enduring. Apart from 
these actual experiences of differences and agreements of 
enduring things, there can be no such thing as Time, unless 
on the exploded doctrine of Realism, nor any self-subsisting 
notion of Time, unless on the erroneous theory of Conceptual- 
itfm. In the absence of objects and states continuing or 
ondurin£, an intuition of Time is a self-contradiction ; in the 



ALLEGED INTUITIVE KNOWLEDGE. 11 

presence of such experiences of enduring things, discriminated 
and compared on the point of endurance, we cannot but have 
an idea of Time. 

Next as to Space, or Extension, the fact common to all 
Matter, and not pertaining to mind. Extension belongs both 
to solid matter, and to the intervals between the masses of 
solid matter, which intervals are measured by the same 
sensibilities, namely, the muscular feelings of motion, sup- 
ported by the passive sensations. 

The a priori philosophers allege that Space comes from no 
experience, but is already inherent in the mind before any- 
thing is perceived; being the condition of our perceiving 
things external. 

In opposition to this view, it is contended that Space in 
the abstract is merely the community or similarity o£ extended 
bodies, and of the intervals between them, commonly called 
empty space. We compare all those things on this particular 
point of agreement; we occasionally think of them under this 
comparison ; and in so doing we are thinking of Space. This 
is the only view compatible with Nominalism. An innate 
form of Space is a species of Conceptualism. 

The pure intuition of Space is said to be the source of our 
knowledge and belief of the Axioms of Geometry, this being 
held to have a character that no experience can explain. In 
the case of these Axioms, the a priori revelation takes the 
form of Principles, and not of mere Notions ; but the fact is 
the same, although differently viewed, f That two straight 
lines cannot enclose a space ;' ' that things equal to the same 
thing are equal to one another :' are held by those that 
contend for an intuition of space, to be intuitive. 

The idea of Cause is included among the alleged intuitions. 
It may be expressed either as a mere Notion or as a 
Principle, namely, i that every effect must have a cause/ An 
equivalent proposition is, * that nature is uniform or that 
what has been will be.' The contention is, that while, by 
experience, we might become aware that particular effects 
follow the law of Cause, or of Uniformity, we could not from 
experience know that every effect has and must have a cause, 
that what has been will always be. 

The idea of Substance means that, underlying all the 
phenomenon or appearances of Matter and of Mind, there is 
an unknown or unknowable substratum, called Substance, 
Noumenon, Permanent Existence. This idea we cannot pos- 
sibly obtain from experience ; the very statement of it, shows 



12 PSYCHOLOGICAL DATA OF LOGIC. 

that it passes beyond experience ; yet some philosophers con- 
tend that we are obliged to assume and believe in it. 

As applied to Mind, Substance is another name for Personal 
Identity, or the supposed continuity of each one's mental 
existence — the canvass that receives and holds together all the 
feelings, thoughts, volitions, that make up the stream of our 
conscious life. 

According to the counter doctrine on this head, the notion 
of Substance is fictitious, incompetent, and unnecessary. The 
real meaniug of Substance, as applied to matter, is the point 
of community of all material bodies, the most highly general- 
ized fact respecting them ; otherwise expressed by Resistance, 
Inertia, Momentum, the Mechanical property of matter. The 
meaning of Substance as applied to Mind is the most highly 
generalized property or properties of mind — the facts wherein 
all minds agree on comparison, and which caused them to 
receive the common designation Mind, as opposed to not-mind, 
or matter. These generalized points of community are 
Feeling, Volition, and Intellect, the three facts attaching in 
various degrees to whatever is accounted Mind. 

The nature of Belief as applied to the controversy respect- 
ing the origin of Knowledge. 

17. There is a natural tendency to believe much more 
than we have any experience of. 

The primitive disposition of the mind as regards belief is 
to suppose that whatever is will continue, that what exists 
here and now, exists everywhere and at all times. This in- 
born credulity is checked and abridged by our experience; 
we soon discover that we have been assuming too much ; and 
by degrees we abate our confidence and adapt our views to 
the reality of things. 

The following are common examples of the tendency. Be- 
fore experience, we believe that as we feel now, we shall 
always feel ; that other people feel as we do ; that what hap- 
pens to us happens to all ; that whatever any one tells us is 
true. By the natural impetuosity of the mind, we form these 
assurances ; experience did not create them, but rather mode- 
rates and checks them. 

That we should treat any partial experience as universal, 
being thus a consequence of blind instinctive forwardness, is 
no proof of what really happens in nature. As we are so liable 
to extend our assertions beyond the facts, we should be par- 



BELIEF PASSES BEYOND EXPERIENCE. 13 

ticularly on our guard against universal declarations. This is 
one of the weaknesses of human nature, and a leading source 
of fallacy and error. 

To make the application tc- the particular case of causation. 
We are very ready to fall into statements as to the universality 
of cause and effect ; but so we do with many other things, 
where we find ourselves utterly wrong. The real evidence of 
the Law of Causation must be something different from our 
being disposed to believe it. 

Nothing can he affirmed as true, except on the warrant of 
experience. 

18. As the natural disposition to believe carries us into 
falsehood, we must, notwithstanding our instincts, cling to 
experience as the only standard of truth* 

This inevitably follows from the nature and sources of 
Belief. Even the supporters of innate principles, at the pre- 
sent day, admit that these principles cannot arise except along 
with the actual things ; a qualification that subjects the innate 
notions as completely to the measure of experience, as if there 
was nothing innate about them. Our intuition of Cause is 
supposed to show itself only when we have observed a number 
of examples of cause and effect ; it is, therefore, involved and 
implicated with our experience to such a degree as to be 
deprived of an independent standing. There is no means of 
discovering what the intuitions would dictate of themselves. 
For all purposes of logical certainty, therefore, they must be 
put out of account ; regard must be had solely to observation, 
and experience. -4— 

Our Knowledge is Limited by our Sensibilities. 

19. We are able to know what things affect our various 
sensibilities, or what may be compounded of these ; and 
our knowledge extends no farther. 

We have a certain number of sensibilities, namely, in the 
Senses (Passive), and in the Muscles (Active) ; and when 
any of these is affected we have knowledge or experience ; 
we know sight, sounds, touches, tastes, smells, and various 
organic affections ; we know resistance and movement. 
We know various emotional states, love, anger, fear, &c. 
We have many experiences from the discrimination and 



H FIRST PUIiNCIPLES OF LOGIC. 

tho aorcement of our various states. In these, we have 

oar 2ph i ie knowable. We can then combine a num- 

..f primitive feelings into a constructive aggregate, as 

n we attain to the idea tf an orange, or of a man. 

or of the entire globe. But we cannot by any effort pass 

8 of these primitive sensibilities. Supposing 

:,) contain powers and properties that do not lm- 

one or other of our senses, as at present constituted, we 

by any means be made cognisant of such properties. 

On this ground the notion of a Substance distinct from all 

attributes is a thing unknowable. We can know body by its 

bio properties, and mind by our conscious feelings, 

thoughts, and volitions ; and we can know nothing beyond. 

FIRST PRINCIPLES OF LOGIC, 

20. In Logic, there are certain general principles, consti- 
tuting it a science properly so called, and lying at the 
foundation of its practical rules and methods. 

These principles are variously expressed. They are termed 
B of Thought, and fundamental Axioms of Reasoning. 
From embracing these highest of all generalities, which pene- 
trate into every science, and from laying down rules on scien- 
tific method, Logic has been designated ' scientia scientiarum' 
— the science that comprehends all sciences. 

The First Principles may be arranged thus : — 

I. The Principle of Consistency, or Necessary Truth. 

II. The Principles of Deduction. 

III. The Principle of Induction. 

I.— Principle of Consistency — Necessary Truth 
21 It is a fundamental requisite of reasoning, as well as 

imnunication by speech, that what is affirmed in one 
in ot words shall be affirmed in another. 

signage often contains equivalent expressions for the same 

>re synonymous names as « round/ ' circular;' a 

1 thing is the same as a circular thing. ' Matter is heavy/ 

_ -ruvitates' are the same fact in different words ; if tho 

so is the other, by virtue of mere consistency. 

d, there are forms that enable us to affirm many separate 

iu one sweeping statement; instead of affirming in detail, 

Mercury moves in an ellipse, Venus moves in an ellipse, &c, 



a 






PRINCIPLE OF CONSISTENCY. lg 



we can put forth the one condensed affirmation — all the planets 
have elliptic orbits. Having advanced this general statement, 
we are required by consistency to maintain each separate 
particular, the orbit of Saturn is elliptical, and so on. 

It is obvious that without this consistency, there could be 
no intelligent communication between one human being, and 
another. Unless the affirmer adheres to his affirmation, how- 
ever he may vary the language, no one can divine what he 
means ; there is no possibility of discussion or reasoning. 

To these self-consistent, although variously worded, affirma- 
tions is applied the descripion c Necessary Truth.' ' All matter 
is heavy, therefore any one piece of matter is heavy ' is called 
a necessary inference. A more exact designation would be 
an equivalent, implicated, or self-consistent assertion. 

There is a vital contrast between passing from one form to 
another form of expressing the same fact, and passing from 
one fact to another distinct fact. When we say — because both 
A and B are mortal, therefore, A is mortal — we merely repeat 
ourselves ; when we say, because A is mortal, therefore B is 
mortal — we make the affirmation of one fact, the ground of an 
affirmation of a different fact. In order to the one leap, we 
need only to know the meaning of language ; in order to the 
other, we must consult the facts of the world. 

The supposition has been advanced that truths of implica- 
tion or consistency, inappropriately called ' Necessary/ are 
drawn out from their equivalent statements by a peculiar 
innate power of the mind, distinct from the powers of observing 
the order of nature ; that without a special instinct they could 
not be evolved, nor reposed in with the absolute credence that 
we give to them. There are no sufficient grounds for the sup- 
position. We should be disposed to consistency of statement, 
without any special instinct. The impossibility of carrying on 
intercourse by language, on any other footing, compels us to 
be consistent in our statements ; at least up to a certain point, 
for we are not always so. There is no instinct needed but the 
broad instinct of self-preservation ; were it not for this we 
should probably care very little about observing the conditions 
of necessary truth. If we could go on as well by maintaining 
an opinion in one form of words, while denying it in another, 
there appears to be nothing in our mental constitution that 
would secure us against contradicting ourselves. Our facul- 
ties as laid down by those philosophers that derive all our 
knowledge from experience alone, taken together with our 
practical necessities, seem quite sufficient to make us ad- 
2 



16 HH8X principles or logic. 

bore to our statements under all variety of forms and expres- 
sion 

22, ii maxims of Consistency known by 

ws of Thought'; they are the principles of 
Identity, Contradiction, and Excluded Middle. 

lo of Identity is given in the form " A is A "; a 
tiling is what it is ; man is man. According to Plato, " The 
lb equal to itself." 
Properly speaking this is not the case contemplated under 
the principle of Consistency ; it is not the same fact in other 
, bat the same fact in the same language. That the 
meaning expressed by the same word or words, is the 
, would appear to be an utter superfluity of affirmation ; 
what we want to be guarded against is mistaking the same 
10 a different form of language. 
This obvious criticism is evaded by giving the law an inter- 
pretation that supposes difference in the statement. The 
ifng is said to be that the thing A, although differently 
won! 1 A ; which is merely an awkward way of stating 

•rural maxim of Consistency. If A equals, or includes, 
. fcc.; then we may say, in slightly different words, A 
* > the whole series of what it includes ; a whole is the 
ram of its parts - a complex attribute is the aggregate of the 
component attributes. 

inciple of Contradiction. ' The same thing cannot be 

this room cannot be both hot and not-hot, that 

Id. Consistency requires that when we affirm a definite 

do not at the same time deny it; having made an 

we are to abide by that. The principle may be carried 

farther. By the law of Relativity, every thing that 

ought of, every affirmation that can be made, has an 

r counter notion or affirmation; to the thing that 

light hue, there corresponds a negative or°oppo- 

W or crooked line. Now thorough-goL 

V requires that when we affirm a certain thSigto be 

i^^^t^^ 116 ™' aS Leibnitz > intend for the 
K nt ^iilT^ t0 *PP rehe -i these judgments of 

of Si I hsafter hlm ' C0nfine the characteristics 

'"glen a d Mfe* ?*T &".*«* judgment* where 

the peculiar^ ff Kan fc mMS? UtMl,y implicated facts. It was 

ung our aetud In rea u e 8 ? ch 8 ^etic judgments 

the proportion that* wo tra S.S ? ** S he instanced > * particular, 

tuo straight lines cannot enclose a space ' 



CONTRADICTION AND EXCLUDED MIDDLE. 17 

a straight line, we must be prepared also to deny that it is a 
bent line ; when we call this man wise, we must also deny that 
he is foolish. This is an equivalent form that plays a great 
part in Logic. Viewed thus, the Law of Contradiction has a 
] regnant meaning, which can hardly be said of the Law of 
Identity. 

The Principle of Excluded Middle. 'A thing must either be or 
not be ;' 'of contradictories one must be true, and the other false.' 

This law grew out, of the distinction of propositions into 
those of total, or universal, and those of partial or particular 
quantity — all men and some men/ When a proposition of 
universal quantity is opposed by one of particular quantity, 
the opposition is not thorough-going ; there is not a perfect 
and entire contrariety. Perfect contrariety is between, * all men 
are mortal ' and 'no men are mortal ;' partial or incomplete con- 
trariety is t all men are mortal,' ' some men are not mortal ;' 
and ' no men are mortal,' * some men are mortal.' Between 
this last species of opposition, there is no middle affirmation ; 
if one is not true, if it is not true that all men are mortal, then 
it must be true that some men are not mortal; we have no 
third alternative. But in the thorough-going contrariety — 
1 all diamonds are precious,' ' no diamonds are precious,' there 
is a middle ground of compromise ; the fact may be that some 
diamonds are precious and some not. Thus, the Law of 
Excluded Middle is an incident of partial or incomplete con- 
trariety. It was enunciated by Aristotle as following from the 
classification of propositions according to quantity. It is too 
much honoured by the dignity of a primary law of thought. 

The Principle of Consistency, inadequately rendered by these 
Laws of Thought, may be assigned as the basis of the logical 
department entitled ' Immediate Inference' (as opposed to 
Mediate Inference or Syllogism), * Inferences improperly so 
called,' * Equivalent Propositional Forms.' Whatever be the 
general designation, the details are fully agreed upon ; the 
doctrine of the Conversion of Propositions is one of the leading 
topics. 

First Principles of Deduction. 

23. In Deduction, there is the application of a general 
proposition to a particular case coming under it. 

The following is a deduction : — ' All arsenic is poison ; now 
this substance is arsenic ; therefore, this substance is poison.' 
This is something more than consistency, implication, or 



18 FIRST PRINCIPLES OF LOGIC. 

equivalence of phraseology. There would be equivalence of 
ailinnation m Baying 4 all arsenic is poison ; therefore, some 
poison*' In the present case, however, we have 
another Btep to take ; we need a second and distinct assertion, 
4 Mm i is arsenic,' before we can conclude, 4 this sub- 

ffattca is poison. Instead of deriving an affirmation from a 
prior affirmation, by change of language, we derive an affirma- 
tion bom iivo prior affirmations ; and these have to be related 
one to another in a proper form, in order that we may draw 
the conclusion. 

This process is called Mediate Inference ; there being an 
intermediate link or stepping-stone between the primary pro- 
portion and the conclusion. We cannot, by mere Consistency, 
resolve 'AH arsenic is poison* into 4 the substance in this 
bottle is poison;' 4 no matter is destructible,' into * no ether 
-tructible ' ; there is in both cases a missing link. Until 
bow that the substance in the bottle is arsenic, and that 
ether is matter, we cannot draw the special conclusions above 
given. 

24. The Axiom, or First Principle, at the basis of De- 
duction, is expressed in a variety of forms, which are 
reducible substantially to two : — 

(1.) Whatever is true of a whole class is true of what can 

-ought under the class. 
(2.) Things co-existing with the same thing co-exist with 
one another. 

There are corresponding forms for negative reasoning. 
The first form is the one suitable to the exposition of the 
syllogism. It sets forth the deductive type of reasoning, as 
-ting of a general principle brought to bear upon a case 
or eases, found to come under it. 

The second form can be shown to be equivalent to the first. 
- the advantage of making prominent the mediate charac- 
ter ot deductive inference, so as to contrast it with immediate 
inference, or mere identical propositions under the Law of 
QCir. Two things not known in themselves to co- 



>hown to co-exist by each co-existing with some third 

thing. Mere consistency will not include this case. Tbe 

pnnciple is admitted as soon as it is understood ; but solely 

each one's experience bears it out. 

The obverse forms, for negative reasoning, are— (1) What 

«b denied of a whole class is denied of whatever can be 



AXIOMS OF DEDUCTION. 19 

brought tinder the class; (2) 'One thing co-existing with a 
Becond thing, with which second thing a third thing does not 
co-exist, is not co-existent with that third thing. 

25. The Axioms of Deduction suppose the Uniformity 
qjL£fct.nre.. 

This is obvious, if the axioms are based on experience. We 
have observed, in a large number of instances, that things con- 
ciding with the same thing coincide with one another ; but 
we have not observed it in all instances ; we have not observed 
it in what took place before we were born, in what is beyond 
our reach, or in what is still to happen. Yet, from the cases 
we have observed, we do not hesitate to extend the principle 
to the unobserved cases. We thus assume that ' nature is 
uniform ; ' that what we find to-day, all circumstances being 
the same, we shall find to-morrow. 

Again, we may deny that the axioms are experimental, and 
call them intuitive. The case is not altered. The intuition 
still supposes nature's uniformity ; the thing intuitively con- 
ceived and believed is not true, unless nature be uniform. 
Thus, on either supposition as to our knowledge of the Logical 
(and Mathematical) Axioms, the truth, still deeper, and more 
comprehensive, is that nature is uniform. The so-called 
axioms, therefore, are not ultimate principles ; they are only 
secondary, proximate, or derivative ; they proceed from a stem 
bearing other branches besides them. If they are true, more is 
true. The wider principle will next be stated, for the sake of 
its other consequences. 

First Principle of Induction. 

26. When we infer from a fact known, to another un- 
known, we make a real inference, for which there must be 
some guarantee. 

The sole guarantee is the Uniformity of Nature. 

Putting a piece of wood into the fire and seeing it consumed, 
we infer that another piece will be consumed in like manner. 
This is to take for granted that what has happened will, in the 
same circumstances, happen again ; in other words, that 
Nature is Uniform. 

The Uniformities of Nature fall under (1) Uniformities of 
Co-existence, and (2) Uniformity of Succession. It is a uni- 
formity of Co-existence that 'inert matter gravitates,' that 
the distinctive property of matter called ' Inertness* is asse- 



ts 



20 FIKST PRINCIPLES OF LOGia 

i tod, through all nature at all times, with the property of 
Weight or (.iravitation. 

evidence for Uniformities of Co-existence is special 
observation of each separate uniformity. From seeing two 
things coupled together in a few instances, we cannot presume 
that they are always coupled together; we must observe the 
frbling in various times, places, and circumstances. If, after 
a sufficient search, we find no single contradictory instance, 
atlirm the union to prevail through all nature. 

In Uniformities of Succession, there has been dis- 
1 a law of Uniformity that shortens the labour on 
enquiry in this department. It is called the Law of Cause 
ami Effect, or Causation. We may express it thus : — 

' Every event is uniformly preceded by some other event :* 
1 To every event there is some antecedent, which happening, 
it will happen/ 

To say that ' Every effect must have a cause/ is begging th© 
question ; the word cause implies an effect, and the word 
effect implies a cause. The correct mode of expression is, ? To 
f event there corresponds a prior event, which happening, 
it will happen ; and which failing, it will not happen/ « The 
antecedent may be, and often is, a whole assemblage of circum- 
stances ; as in the case of Health, an effect depending on 
many conditions. 

Since there are effects produced by a plurality of Causes, the 
principle of Uniformity is limited and qualified by that circum- 
stance. Thus, Death may be caused by starvation, by a 
violent blow, by poison, &c. It is therefore proper to say 
that given any of these conditions in sufficient amount, death 
will lullow ; but the occurrence of death does not prove that 
tncre has been starvation; it proves only that one of the 
producing agencies has been present. In the Inductive 
enquiry into nature, all the causes that may produce each 
eih-et are sought out. 

hVom the Law of Causation, we deduce consequences such 
— II the cause be absent, the effect will be absent'— 

, :,;; i11 h: prCSent ' 'Whatever agent cannot be 
cd , lt hout the cessation of the effect, must be the cause 

with u fl PIT 8 "' ^T hat ' Ver a ^ ent can be rented 

iu e and effiS 5? ^ is n0t the ca *< 'The 

cause and effect vary proportionately/ 



LAW OF CAUSATION. 21 

These various aspects or implications of the Law of Causa- 
tion are the maxims serving to eliminate and to prove cause 
and effect in the phenomena of nature. 

28. The Law of Uniform Causation appears in a form 
still more pregnant with consequences, namely, the Law of 
the Persistence, Conservation, Correlation, or Equivalence 
of Force. 

This is a generalization only recently effected. 

Galileo and Newton may be considered as having established 
the Law of the Persistence or Conservation of Mechanical 
Force, that is, force applied to matter in masses. If one ball 
strikes another and puts it in motion, the force imparted to 
the second is exactly what is lost to the first. 

Lavoisier established the persistence of ponderable matter, 
showing that no atom of matter could be destroyed, and none 
created. In burning and in evaporation, the particles merely 
change their positions ; they do not abandon their material 
properties of inertia and gravity. 

In the present day, evidence has been obtained to show that 
oilier forces besides mechanical force, namely, Heat, Chemical 
Force, Electricity, Nerve Force, have the same numerical 
persistence ; they can neither be created nor destroyed ; 
They can, however, be mutually converted, at a definite rate. 
Heat can give birth to Mechanical Force ; Chemical Force can 
evolve Heat ; Electricity is convertible into all the other 
modes. In this conversion, nothing is lost, and nothing is 
created ; when heat becomes a mechanical prime mover in the 
steam engine, it disappears as heat. When mechanical force 
is seemingly destroyed, as when a cannon ball spends itself on 
an unyielding mass of stone, the whole momentum of the ball 
is transformed into heat ; at the place of encounter, both the 
ball and the stone are raised in temperature, exactly in propor- 
tion to the momentum arrested. 

This great law of the quantitative persistence of Force, or 
Momentum, deserves an eminent place in the Inductive Logic. 
It encompasses and pervades all the natural sciences, each 
one of which is but a partial development of it. 

NATURE AND CLASSIFICATION OF KNOWLEDGE. 

29. Knowledge is made up of affirmations respecting 
the order of the world. These affirmations are the subject 
of Belief, of which the ultimate criterion is Action. 



V 



22 NATUKE AND CLASSIFICATION OF KNOWLEDGE. 

Twice two is four; the sun rises and sets; unsupported 
bodies fall to the ground; heat causes water to boil ; animal 
bodies are nourished by food and air ; harmony is agreeable 
to the mind :— are affirmations, or Knowledge, respecting the 
universe. We believe them, and show our belief by acting on 
them. When we desire water to boil, we apply heat ; which \ 
is our belief of the affirmation. 

30. The first requisite of Knowledge is that it shall be j 

true. 

An Affirmation is true when, on actual trial, it corresponds 
to the fact. This is the direct proof. Indirectly, we may 
test the truth of affirmations by comparing one with another. 
Wherever there is contradiction, there must be falsehood. 

31. Knowledge is either Particular or General. 

An Affirmation respecting a certain individual thing, as 
* this house is stable/ ' Caesar was brave,' ' a certain patient 
will not recover ' — is a particular or individual affirmation ; 
it is limited to one subject. An affirmation respecting a whole 
class or species of things — as ' an erection is stable when the 
line of the centre of gravity falls within the base ' ; * all great 
generals are brave ' ; 'the stiffening of the limbs is a sign of 
death ' ; — are general affirmations ; they extend to instances 
beyond number. 

32. Owing to the frequent recurrence of the same things 
and the same processes, we can attain to numerous genera- 
lities. 

If every individual thing in nature were throughout unique, 
resembling no other thing, each would need a law to itself. 
If, instead of a common substance ' water ' in all seas, rivers, 
and fountains, there were a thousand different substances, we 
should have to multiply affirmations accordingly. If, instead 
of the sixty-three elementary bodies known to us at present, 
the globe were made up of six thousand elements with their 
compounds, there would be a great increase in the bulk of our 
knowledge. If instead of sixtv-three, there had been six, we 
should have been able to comprehend all physical knowledge 
in comparatively few affirmations. 

33. It is desirable to attain knowledge in the highest 
possible degree of generality. 



TRUTH AND GENERALITY. 23 

The reason is obvious. A general affirmation is a great 
many particular affirmations in one. It is a vast economy of 
the human understanding. A general law places us at a 
commanding height, where, by one glance, we can survey a 
wide array of facts. The law of Gravity, the law of the Per- 
sistence of Force, the law of Definite Proportions in Chemistry, 
the law of Relativity in Mind, — severally comprehend thou- 
sands of individual affirmations. 

34. The perfect form of knowledge is Science. 
The peculiarities of Science are these : — 

I. It employs special means and appliances to render 
knowledge true. 

The uninstrncted man is apt to make affirmations without 
taking the trouble to test them. The scientific man, on the 
other hand, not only avails himself of the common means of 
proof, but employs an express machinery for testing all the 
knowledge in his own department. This machinery is to a 
certain extent common to all knowledge, and all science ; and 
to a certain extent, it is special to each science. The common 
machinery is embraced in Logic. 

35. II. Knowledge, in the form of Science, is made as 
general as possible. ' 

Science does not refuse individual facts, provided they are 
true ; on the contrary, it collects as many such facts as pos- 
sible. But considering the enormous sweep and vantage 
ground of generalized facts, science pushes the generalising 
process to the utmost limits. A few isolated facts carefully 
ascertained to be true, would be valuable in themselves, but 
they would not constitute a science. 

36. III. A Science embraces a distinct department of 
the world, or groups together facts and generalities that 
are of a kindred sort. 

It appears, on investigation, that the operations of the world 
are different in their nature, and need to be differently studied. 
The forces that maintain the motions of the heavenly bodies, 
are different from combustion, magnetism, or vegetable and 
animal growth. The functions of the mind scarcely resemble 
anything else. Hence the affirmations or truths respecting 
the world fall into distinct departments ; and there is an evi- 
dent propriety in observing the distinction, and in classing 
kindred facts together. To class together facts about the 



24 NATURE AND CLASSIFICATION OF KNOWLEDGE. 

planets, and facts about the human mind, could only perplex the 
understanding. 

37. IV. A Science has a certain order or arrangement of 
topics, suitable to its ends in gathering; in verifying, and in 
communicating knowledge. 

Besides bringing together the facts and generalities relative 
to each division of phenomena, a science must present its 
materials in a fitting arrangement. 

This arrangement varies in the different sciences. Still, in 
all of them, attention must be given to the following points — 

(1) To proceed from the more easily, to the less easily 
known. If any fact or generality depends upon or presup- 
poses another, that other should be stated first in order. 

(2) Whatever is requisite for proving any doctrine should 
precede what is to be proved. In concatenated or deductive 
sciences, like geometry, each affirmation depends upon some 
that go before ; and the evolution is thus methodical and sys- 
tematic. 

(3) The meanings of all terras should be distinctly given 
before they are made use of. . It is usual to commence with 
the definitions of leading terms. 

38. The classification of the Sciences is in accordance 
with the foregoing views. In the first place, it follows the 
division of nature into departments, and in the second 
place, it follows the order of relative simplicity and of 
mutual dependence in those departments. 

If each different process of nature were entirely separate 
from the others, there would be no special order of the sciences. 
But the distinct powers — gravity, heat, animal growth, mind, 
&c , are to a great degree intermingled in their workings. 
Moreover, all phenomena whatever are subject to laws of 
Quantity, and these can be studied apart from any one class of 
things ; hence, such laws are a preparation for all the depart- 
ments. Nor is this the only way that one science paves the way 
for another. Accordingly, there is, among the several sciences, 
an order of dependence that, to a certain degree, determines 
their succession to the learner, and their gradual evolution 
under the hands of scientific enquirers. 

39. The Sciences are either Abstract or Concrete. 

The Science of Mathematics, which treats of quantity, with- 
out referring to any particular kind of quantity, as length, 



OEDER OF THE SCIENCES. 25 

weigh t, heat;, &c, is called an Abstract Science. With one 
exception, it is the most abstract of all the Sciences ; the pro- 
perties treated of are the most general of all properties ; and 
they are discussed in the highest degree of separation from 
concurring attributes. 

On the other hand, Zoology, which classifies and describes 
one great department of actual or concrete things — the whole 
Animal Kingdom — is a Concrete Science. 

The science that, in point of abstractness, rivals Mathema- 
tics is Logic itself. The First Principles of Logic, as above 
laid down, including the law of Consistency, the law of Deduc- 
tion, the law of Uniformity, are paramount over every 
science ; they are wider than even the laws of quantity. 

Next to quantity, the most general attribute of natural 
things is motion. All material bodies may pass into motion — 
motion in mass (molar movement) or motion in molecule 
(molecular movement) or both. Now the laws of motion may 
be laid down without reference to any particular objects- 
Hence there may be an abstract science of Motion, for which 
the name might be Abstract, Theoretical, or Rational 
Mechanics ; the designation now accepted is * Kinematics. I 
The principles of motion, as applied to actual bodies — solids, 
liquids, and gases — constitute the departments of Concrete 
Mechanics, which have appropriate names. 

The Abstract is also the simple, the concrete is usually the com- 
flex. When what is true of the Abstract is not also true of the 
concrete, the reason is an incident and not a necessity. What is 
true in the Abstract really means truth in the concrete ; the 
abstract is merely a name for the concrete under agreement. A 
law true in the abstract would be a contradiction, if it were not 
true in the concrete also. But in the concrete, there may be 
counteracting forces, so that the real point is to contrast a 
power working alone with a power working in company. The 
abstract law of motion — the persistence of a body in its present 
state, fails in the concrete, because of friction, or of opposing 
obstacles ; the tendency to persist is compounded with other 
influences, and we have to calculate the result of the composition. 
Self-interest working alone would have certain consequences ; as 
an element of a compound, it is no longer accountable for the 
whole effect. 

The Abstract Sciences properly precede the corresponding Con- 
crete Sciences. 

40. For the purposes of the present day, the Sciences 
may be classified as follows : — I. Logic, II. Mathematics, 
III. Mechanics or Mechanical Physics, IV. Molecular Phy- 



2G KATUBI AND CLASSIFICATION OF KNOWLEDGE. 

bu'8, V. Chemistry, VI. Biology, VII. Psychology. In 
i n * of these, there is a distinct department of pheno- 
B ; taken together, they comprehend all known pheno- 
mena ; and the order indicated is the order from simple to 
complex, and from independent to dependent, marking the 
order of study and of evolution. 

I. Logic embraces, as has been seen, the most fundamental 
and universal of all principles — Consistency, Deduction, and 
Uniformity. It reposes upon nothing more fundamental than 
itself, and it gives foundation to all the other sciences. There 
can be no science without assuming all the data of Logic, 
whether avowedly or not. 

II. Mathematics is the abstract science of Quantity, and the 
of Quantity, in every possible combination. 

III. Mechanics, or Mechanical Physics, or Mechanical 
Philosophy, is the science of Motion, as regards bodies in 
mass, and of Force, which is the momentum of moving masses. 
There is an abstract or theoretical department (Kinematics), 
comprising all the laws of the Equilibrium, and of the Move- 
ments, of matter in mass, without reference to any special 
class of things. The Concrete applications of these laws 
embrace Astronomy, or the Celestial Motions, the kindred 
subject of Falling Bodies on the Earth, Statics, Hydrostatics, 
Dynamics, Hydrodynamics, Acoustics. 

IV. Molecular Physics refers to the molecular movements 
and arrangements of material bodies. It comprises the Mole- 
cular Cohesions and Adhesions, as operative in the structure 
of Solids, Liquids, and Gases ; Heat ; Light ; Electricity. 

V. Chemistry is a continuation of Molecular Physics, having 
more especial reference to the Combinations and Decompos£ 
tions, named chemical, and characterised by great accompanying ] 
changes of properties. I 

The branch of Science, long known as Natural Philosophy, 

rises both Mechanical Physics and Molecular Physics, but 

excludes Chemistry. An equally, if not more, suitable arrange- 

would be to treat Chemistry as a part of Molecular 

} MCS ; i nto 7 lnch lt sha <les by imperceptible gradation. In 

point ot tact Chemical action is inseparably implicated with 

and with Electricity, although these subjects can be, in 

d. detached from Chemistry 

exltnt an n Ca ,\ P1, 7 SiC / and Molec ^' ^ysics, taken together, 
SSLS^l < Undamental as Pect* of the great doctrine of 
the Iersistence, Conservation, or Correlation of Force. 



CLASSIFICATION OF THE ABSTRACT SCIENCES. 27 

VL Biology enters npon an entirely new field of pheno- 
mena, the phenomena of Life, or of Living Bodies, involving 
an organised structure, with perpetual evolution and repro- 
duction. This science is posterior to the foregoing, inasmuch 
as living bodies come under all the laws of Mechanical and of 
Molecular Physics, in addition to their own specific laws as 
living bodies. 

Biology is divided into Vegetable and Animal Biology ; the 
one exhausting the structure, classification, and description of 
Plants, the other referring to Animals, Botany, Zoology, 
Human Anatomy and Physiology, are the concrete depart- 
ments of Biology, and its leading divisions for study. There 
can scarcely be such a science as Abstract Biology ; the laws 
of life cannot be given in separation from living vegetables and 
animals. The nearest approach to a division into Abstract 
and Concrete, is the distinction between Physiology— -Vegetable 
and Animal — on the one hand, and the classification and de- 
tailed description of Plants and of Animals on the other. 

VII. Psychology, or the Science of Mind, is a unique de- 
partment of natural phenomena. Its terminal position in the 
order of the Sciences is owing to two circumstances. In the 
first place, it is a subject of great complication, aggravated by 
an especial amount of corrupting bias. Hence the student 
does well to come prepared with a scientific discipline, such as 
is best furnished in the previously ennumerated sciences. 
Secondly, although the mind proper — the subjective conscious- 
ness — is a unique subject, yet a material organism is allied 
with it throughout, and therefore should be known as so allied. 
ISTow the material organism falls under the last part of Biology, 
namely Human Physiology. 

These seven branches contain the laws of every known pro- 
cess in the world, whether of matter or of mind ; and set forth 
those laws in the order suitable for studying and comprehend- 
ing them to the greatest possible advantage, No phenomenon 
can be strange to any one thoroughly conversant with those 
subjects. Properly speaking, the laws of the phenomena might 
be comprehended under four heads : — Molar Mechanics, Mole- 
cular Mechanics (or Physics), Biology, Psychology. Logic 
and Mathematics are merely aids to the better comprehension 
of the actual things. 

Astronomy was detached, by Augnste Comte, from its usual 
position under Mechanics, and made one of the primary depart- 
ments. His reason was that it deals with the great fact Gravity 
— a distinct and specific phenomenon, unlike everything else, 



28 NATURE AND CLASSIFICATION OF KNOWLEDGE. 

and capable of being developed apart, merely with the aid. of 
Mathematics and abstract Mechanics. Although the position 
thus given to the subject may be thought unnecessarily pro- 
minent, yet the reason contains an undoubted and highly illus- 
trative fact. The gravitating action is peculiar and distinct ; 
it operates in the celestial bodies uncomplicated with any other 
actions, giving Astronomy a character of remarkable simpli- 
city as regards the forces at work. 

41. The Concrete Departments include various additional 
subjects — as Meteorology, Mineralogy, Geology, Geography, 
— no one of which involves any operation but what i? 
expounded in the Fundamental or Departmental Sciences. 

In each of these branches, a certain group of locally allied 
phenomena is separated for special study. Meteorology, treats 
of the Atmosphere, all whose phenomena are regulated by 
the laws of Mechanical and of Molecular Physics. The same 
may be said of Mineralogy ; there is no natural agent at work 
in the formation of minerals, but what is discribed in the 
fundamental departments last named. The special aim of the 
subject is to provide a systematic mode of classifying and 
describing mineral bodies, so that they may be recognised and 
understood. Geology involves Biology, in addition to Physics ; 
its localit) is the crust of the globe, so far as accessible. (7eo- 
gra-pJiy is the science of the Earth's surface — and is, like the 
two foregoing, a descriptive science, but containing no new 
laws of phenomena. 

Among Concrete Sciences related more particularly to 
mind, we may class the Science of Society, Politics, or Sociology, 
which applies the laws of Mind to human beings aggregated 
in Society. Another example is Philology, or the theory of 
Universal Language, together with the Classification of the 
Languages now or formerly spoken. 

42. We have not yet exhausted the branches of know- 
ledge designated Sciences. There remain the Practical 
Sciences. 

The final end of all knowledge is Practice, or the guidance 
of conduct. There are numerous departments of practice, 
according to the needs of human beings ; and every one of 
these reposes upon knowledge more or less accurate. Another 
name for practice is Art. 



PRACTICAL SCIENCES. 29 

Now, according to the quality of the knowledge at com- 
mand, Art may be empirical or it may be scientific. An 
empirical art proceeds solely upon the knowledge gained in 
the exercise of the art itself. All arts were empirical before 
science began ; as for example, Agriculture, Navigation, and 
Metallurgy. There are still some empirical arts, as the greater 
part of Medicine. 

Art becomes scientific, when science is brought to bear 
upon it Navigation is a remarkable instance ; being aided 
by Mathematics, Mechanics, Astronomy, Optics, and Meteoro- 
logy. Engineering, Building, Machinery, Dyeing, and the 
range of Manufactures generally, are arts founded on Science, 
and may be called Scientific Arts, or Practical Sciences. 
Another group (connected more with mind), includes Ethics, 
Logic (in its practical aspect), ^Esthetics, Rhetoric, Grammar, 
Education, Politics, Jurisprudence, Law, Political Economy. 

Several of the subjects last named might be viewed either 
as Theoretical Concrete Sciences, or as Practical Sciences. 
This would depend upon whether they were constructed most 
upon the one type or upon the other. Thus, Politics might be 
arranged as a methodical body of political doctrines consecu- 
tively evolved from primary truths or data, like Mechanics, 
Chemistry, or Psychology. It might also be arranged with a 
predominant regard to the political end, and might take the 
form of a series of maxims or directions for the art of govern- 
ment, more or less supported by scientific doctrines and 
general reasonings. A similar remark applies to. Political 
Economy, Jurisprudence, and Ethics. 

43, In a Practical Science, the knowledge is selected and 
arranged purely with reference to the object in view. The 
definition of a Practical Science is its End. 

This makes a great difference as respects choice of topics, 
between a Theoretical Science (Abstract or Concrete) and a 
Practical Science. In the first, the knowledge imparted per- 
tains exclusively to one department of natural phenomena — 
Motion, Life, Mind, &c. In the second, the knowledge is 
selected from one or more theoretical sciences, and set forth in 
the order suited to the end in view. In a theoretical science 
we obtain, in the most succinct and intelligible shape, the en- 
tire body of existiug information relating to one group of 
kindred phenomena ; the knowledge being applicable to 
several arts, but not specially applied to any. In a practical 



30 NATURE AND CLASSIFICATION OF KNOWLEDGE. 

nee, the information conveyed is kept in subservience to : 
the purpose of the art. § 

That the definition of a Practical Science is its End, was a 

p ,; j agisted upon in the Aristotelian treatises. Thus, in 

Ethic ve to ascertain first the feZos, the ethical end ; on 

the chief differences of opinion on the subject. 

, in so far as being a theoretical science, is defined by its 

i merit ; as a practical science, or an art (whether 

irical or scientific), it must be defined by its end. (See 

Appendix A, and Inductive Logic, Book III.) 

DOTKRKNT VIEWS OF THE DEFINITION OR PROVINCE OF 

LOGIC. 

44. Logic has been termed (I.) the Art of Reasoning 
and (11.) the Art and Science of Reasoning. 

The first is Aldrich's definition; the second is Whately's 
amendment. In both forms, there is an admission of the 
practical character of Logic ; in the second form, the practice 
is said to be founded on Science ; in other words, Logic is a 
Practical Science. 

45. The term ' Reasoning ■ is insufficient, as being, first 
lible of more than one interpretation, and, secondly 

too narrow for the admitted scope of Logic. 

Reasoning may mean Deduction solely, or it may mean 
Inference as a whole, which is Deduction together with Induc- 
tion. In the narrower acceptation, Logic would be confined 
to Deductive Reasoning, or Syllogism ; in the wider accepta- 
tion, it comprises Induction also. The narrower meaning has 
Been the most usual in Logical treatises, but in scarcely any 
one is it consistently adhered to. Either under the title of 
Induction, or as Applied Logic, matters pertaining to Induction 
have been introduced by Whately, Hamilton, Thomson, and 
oihi 

kin, taken in its widest sense, the term Reasoning is still 

row. We always find, in books on Logic, subjects not 

omprised under the term Reasoning: as Classification, 

Definition, and Division ; all which are amenable to rules, and 

y be performed well or ill. We apply the epithet ' logical ' 

to a definition, as well as to an argument. 

4G. lit Logic has been described as ' the Science of the 
Laws of Thought.' 



LAWS OF THOUGHT. 31 

This definition remedies the narrowness of the foregoing in 
respect of the use of the word Reasoning. ' Thought ' is large 
enough to cover all the processes admitted into Logic. It, 
however, does more ; it includes in its meaning all the intel- 
lectual processes, being co-extensive with intelligence itself. 
Memory and Imagination would be departments of thought. 
Consequently, the word has to be narrowed in its signification, 
to what is termed ' Discursive ' or * Elaborative ' Thought, the 
faculties concerned in the scientific operation, or in the attain- 
ment of truth ; which faculties may be summed up in the two 
— Abstraction and Reasoning. The power called Abstraction 
covers those portions of the field of Logic that Reasoning in 
its widest meaning does not cover. 

Even with this limitation, the title ' Laws of Thought ' is 
liable to other objections. In particular, it points, by an 
obvious interpretation, to Psychology rather than to Logic. 
The Laws of Thought, or of Thinking, would appear most 
naturally to indicate the laws of the rise and succession of our 
thoughts as explained in Mental Science ; in other words, the 
laws of the Association of Ideas. 

This difficulty can be met only by arbitrary interpretations 
of ' Laws of Thought.' By some, the phrase is qualified by 
the word * Formal, ' which, however, does not relieve the 
perplexity. Do the ' Laws of Thought ' mean Thought as it 
is, or Thought as it ought to be ? If ' Thought as it is/ then 
the subject is pure psychology ; if ' Thought as it ought to 
be,' there must be supplied some principle for checking or 
controlling the spontaneous thinking of the mind, which 
principle is the all-important element of the case, and needs to 
be explicitely stated. 

Hardly any amount of explanation will convert into a good 
Definition a phrase of such ambiguous and uncertain scope as 
the * Laws of Thought.' When the proper limitations are 
supplied, there can be found some other phraseology more 
suitable to indicate what is intended. If the meaning is 
4 Thought as it ought to be' — Right or Corrected Thinking, — 
a standard must be assigned, which standard can be nothing 
but the standard of what is true and false; ' the end of thought,' 
Hamilton remarks, is * truth.' 

47. IV. Logic is defined (Port Royal Logic) 'the Science 
of the operations of the understanding in the pursuit of truth.' 

Here three things are implied. First, Logic is a department of 
practice, scientifically conducted, that is, a Practical Science. 



VIEWS OF THE DEFINITION OF LOGIC. 

Secondly, v. very Practical Science, and every Art, 

not, mast have an End, the end of th- 

the attainment of Truth.^ Thirdly, tJ 

.a this pursuit is an enquiry into the oper 

. .in understanding. 

i positions can hardly be controverted, Logic, 

; tain theoretic aspect, to be considered pre- 

fcbief aim must ever be practical. Had the sub- 

n anted as an aid to the search of truth, it would 

beet called into existence. 

n — that the means in Logic consists in an 
I ne operations of the Understanding — admits of 
ism, Tins may be a means, but is not necessarily 
means, 

. The foregoing definition is modified by distinguish- 
ing between two kinds of truths: — namely those known 
Uely t intuitively, or by direct consciousness; and 
known by the mediation of other truths. 
The distinction is fundamental and important. Facts of 
I onsciousness, as — I am hungry, I hear a sound, I am 
led, I am speaking,— are amenable to no laws or rules ; they 
:ial and conelusive of themselves. We cannot escape from 
not be more or less convinced of them by any 
method of procedure. They are the ultimate data of each 
I knowledge, 

i»er elass of truths, by far the most numerous, are 

>t by direct, immediate intuition, or consciousness, 

8 medium of some other facts, themselves immediate. 

has risen is a mediate or indirect truth ; what is 

the sensation of light, and from that immediate 

der or -believe the other fact, ' the sun is above the 

That I feel cold is an immediate truth, that another 

"Id is a mediate inference ; the immediate fact 

sations of sight, or of sound, with which I 

I connect the fact of feeling cold. All the feel- 

*ud thoughts oi other beings are known to us in this 

• that is transacted in our absence must be known 

* all. And as intuitive knowledge is 

»e present, all knowledge of the past and of the 

dy mediate, 
nate truth is properly an Inference. When a 
bmg .s known, not ,u uself, but by some second thing related 



IMMEDIATE AND INFE11RED THUTHS. 33 

to it, the knowledge is mediate or inferred ; and the immediate 
fact is the Proof or Evidence of the fact so inferred. The fact 
that the air is below 32 deg. Fahrenheit, is inferred from 
the visible phenomenon of falling snow ; the snow is 
the medium of inference, the proof or the evidence that the 
air is cold ; the melting of the snow would be the proof that 
the air is becoming warmer. 

All such inferences suppose a sure link of connexion between 
different phenomena. If A is the evidence of B, A and B 
must be known as joined together in the nature of things. 
Now, in order to our assurance of such connecting links, 
certain processes have to be gone through — namely, Observa- 
tion, Induction, or Deduction. In performing these processes, 
we are liable to commit mistakes ; we need a number of 
precautions ; and these precautions are the rules of Logic. 

As regards Immediate Truths, no such precautions or rules 
are necessary. The chief mistake that we are liable to on 
their account (and the mistake is a frequent source of error) 
is the confounding of an immediate truth with an inferred 
truth. We are apt to say that we are immediately conscious 
of what we only infer. The most notable instance is our 
belief that we see distance ; whereas, in fact (according to 
Berkeley and the majority of scientific men), we do but infer 
distance ; our immediate consciousness is only of colour and of 
the tension and the movements of ocular muscles, which are 
signs of distance, but are not themselves the fact of distance. 

Thus, while there are certain things, admitted by all to be 
matters of intuition, or immediate consciousness, such as 
our sensations and emotions in their primitive character ; and 
certain other things equally admitted to be matters of 
inference, or mediate cognition, such as the feelings of other 
men, the facts of testimony, and the generalizations of science ; 
— there is, as often happens, a middle ground, or margin, 
where intuition and inference are blended and confused, and 
I where what is accounted intuition by one man may be called 
inference by another. This happens with some of the most 
celebrated questions. The existence of the Deity is reckoned 
by some to be an intuition, or an immediate revelation of 
consciousness, a judgment a priori ; by others an inference 
from design, or a judgment a posteriori : while most commonly 
it is viewed as both the one and the other. Again, our 
perception of a material world is accounted an intuition by 
Keid and Hamilton ; while others deny it to be intuitive in 
the sense intended. In fact, the controverted questions 



VILWS OF THE DEFINITION OF LOGIC. 






Origin of our Knowledge all lie upon the 

t intuition and inference. 

deals with truths of Inference solely, 

cording to Mill, amending the foregoing 

hould be ' the science of the operations of the 

oding that are subservient to the estimation of 

ion of Evidence mnst unquestionably he accounted 

.im function of the Logician. It is his business to lay down 

»ti of true and fake, with a view to the establishment of 

• rue. 

tt her the Logician should give suggestions as to dis- 

to the modes of arriving at suggestions to be 

e logical tests, is an open question. Mr. Mill 

include this in his definition, but in the title 

I w«»rk he couples with the ' Principles of Evidence* the 

of Scientific Investigation ' 

In the present work, Logic is viewed— 

a Theoretical Abstract Science, 
"inlly, as the Practical Science of Proof or Evidenca 
Thirdly, as a body of Method auxiliary to the search 
Truth. 

Logic, as we bave seen, lays down the most funda- 

"f all affirmation, and deduces inferences from 

mbodying them in suitable formulas. In this 

parallel of Mathematics, being equally a theo- 

. although greatly inferior to Mathematics in the 

of its developments and amplications. The 

yllogistic forms may be regarded as a theorizing 

forms being systematically deduced from the 

or axioms, of Deduction. From the Inductive 

on, m like manner, are deduced inferences, con- 

■ nous of inductive elimination. 

-ic in this theoretical aspect, the older 

■ Led Lngica docem, the ' teaching' and specu- 

. ' «tens, the • guiding ' and practical side. 

h'rgnn and Boole may be considered as 

'he theorencal development, and as illnstrating 

i allehsm between Logic and Mathematics-the 

• pre-eminence. 

■ « the Practical Science of Proof or Evi- 
Uistons of Theoretical Logic are of value in 



LOGIC AS THE SCIENCE OF PltOOF. 35 

discriminating between truth and falsehood, between sufficient 
and insufficient evidence. This is the useful part of Syllogism, 
of Inductive Elimination, of the theory of Definition, and so 
on. The immense theoretical developments of De Morgan and 
Boole pass beyond the known applications of Logic in the 
present state of our knowledge ; although, like the Conic Sec- 
tions, which lay unused for two thousand years, these elaborate 
formulaB may one day be turned to practical account. 

In the present work, the laws of Evidence are regarded in 
their widest compass, or as embracing alike Deduction and 
Induction. The main reasons are — that Induction is, properly 
speaking, the foundation of all knowledge ; that errors are 
frequent in the Inductive processes, and are as much amenable 
to rules and corrections as errors of Deduction ; and that the 
utility of a Logic strictly confined to Deduction is comparatively 
small, so much so that writers on the science seldom 
confine themselves to this department. (For a full considera- 
tion of the conflicting opinions as to the Province of Logic, see 
Appendix, B.) 

Thirdly. Logic is a, body of Method, or Procedure. It may 
without impropriety give an account of all known processes 
that aid the understanding, whether in proving or in evolving 
truth ; provided always that these are of a general kind, 
adapted to all science or knowledge as such, and not mixed up 
with the technical specialities of the separate sciences. 

There are various admitted uses of Logic that fall under 
Method. One of these is expressed by Hamilton as * the ren- 
dering explicit in the statement, whatever is implicit in the 
thought/ In ordinary reasonings, there are frequent omissions 
or ellipses ; and in cases of difficulty or obscurity, these omis- 
sions need to be supplied. 

The second point belonging to Method is the arranging of 
an argument or chain of reasoning into the form that best 
discloses to the mind its conclusiveness or inconclusiveness. 
This is one great use of the Syllogism. But it is not confined 
to syllogism. The Inductive canons give a full and precise 
account of all the possible modes of proving a fact inductively ; 
and by reducing any given proof under its proper heads, we 
see better what it amounts to. By the same canons, we are 
also taught what sort of proofs we ought to look out for and 
produce in any given instance. 

Once more. There are certain modes of presenting to the 
mind all the known facts and premises of a subject, such as to 
suggest the conclusions involved, and to bring into explicit 



M DIVISIONS OF LOGIC. 

at is implicit and latent. This is a positive aid 

of tlio Association of Ideas may be applied to 

[active, and in Inductive discoveries. The 

lactive Science is, from a given number of 

or principles, to evolve the greatest number 

be intellectual forces are greatly assisted by 

n forms of procedure. 

1 resume, in a final Appendix note, all the bearings 

1 Method, as an Art of Discovery. 



DIVISIONS OF LOGIC. 



51. hi tli" discovery and verification of knowledge, there 
ur cardinal operations ; one relating to Facts, and the 

the ( reneralizing of Facts. They are, I. Observa- 

iluding Experiment : II. Definition, or Abstrac- 

: U. Induction ; IV. Deduction. 

Observation. 

52. If there were rules of observing common to all 

and subjects, Observation would be a part of the 
linL >gic. 

ining matters of fact, which must be the ground- 
work of all scientific doctrines, we must have recourse to 
Observation and Experiment. As regards the material world, 
- the exercise of the Senses ; as regards the 
ind, it supposes Self-consciousness, 
all the cardinal processes, Observation is the least 
i Logical systems. If it were wholly, as it is in 
r of pure intuition, it must be for ever excluded 
,ic. In reality, however, it is something more than 

ran a Tact,* or an c observation' is seldom an ab- 

e or individual conscious impression. We speak 

bigh water at Leith follows high water at 

&n definite interval ; but this is far beyond 

.1 impression upon our senses. It is a generality 

mpass, the result of the comparison of many 

It is a fact only by reference to some 

to the laws of tidal succession over the 

globe lucre is a process of induction requisite in order to 

••tabhsn 8nch a fact j and all the securities for soundness in 



ARTS OF OBSERVATION. 37 

the inductive proofs are called into play. So the fact that the 
barn-door hen brings forth her young in the egg is an induc- 
tive generality ; innumerable observations have contributed to 
its establishment. Only, there are generalities still wider, of 
which it is an individual constituent; but the difference is 
merely the difference of lower and higher degrees of generaliza- 
tion. 

We come, in the last resort, to observations that are strictly 
individual. Such are historical incidents ; the taking of Jeru- 
salem was an individual fact. So, the details of scientific 
observation are individual acts of sense and attention. They 
are not, however, intuitions ; for when we say we observe the 
the needle pointing to the north, we include with the impres- 
sion made on our senses a number of inferences from previous 
knowledge. It is from previous knowledge that we know 
we are looking at a needle, and that its direction is north. 
The simplest observation is thus a mixture of intuition and 
inference ; and our habit of joining the two is one cause of 
error in the act of observing. 

There must be in all observation (of the material world) an 
exercise of the senses; accuracy of observing is accuracy of 
sense discrimination. Now the delicacy of the senses is partly 
natural, partly the result of their exercise upon the special 
objects. The astronomical observer is trained in the observa- 
tory ; the physicist and chemist in the laboratory ; the anato- 
mist in the dissecting room ; the naturalist in the field, or the 
museum ; the medical student in the hospital. 

Besides the discrimination by the senses, a good observer is 
trained to avoid delusive mixtures of inference with observa- 
tions. He is also indoctrinated in certain artificial rules and 
precautions for attaining the highest possible accuracy ; such 
as the repetition and comparison of observations, the striking 
of averages, the elimination of causes of bias in the instru- 
ments ; to these are added certain mathematical formulas of Pro- 
bability, which contribute still farther to the certainty of observed 
facts. Still, these rules are, for the most part, peculiar to the 
different subjects. 

It is in like manner a special accompaniment of each de- 
partment to know what to observe ; to select from a miscellane- 
ous group the circumstances in point. The ongoings of a 
nation are multitudinous as the sands of the sea shore ; the 
politician or historian knows what to fix attention upon and 
to record as political facts, the data of political science. The 
designations applied to the power of political observation are 



H DIVISIONS OF LOGIC. 

< jpp, sagacious and discriminating judg- 

ing.' No art or rules can impart 
i*l attributes thus described. 
rations might be given of the errors in observa- 
I >y untutored minds. Still, the best 
ral observation would be a training in 
Every educated person should know 
the practical manipulation of at least one of the 
at ion or experiment — such as a Natural. 
Physics, Chemistry, or Physiology. 
Logicians, in dissenting from the inclusion of Induc- 
of Logic, have remarked that the rules of 
Induction must be special to the separate sciences. This is a 
: of the remark just made as to observation. But the 
the same. The methods of Induction do not 
in the different .sciences, as the methods of Observation 
Induction in Astronomy is the same as Induction in 
try, in Physiology, or in Psychology; the distinctions 
in the Inductive problem are distinctions that do not divide 
Inductive sciences. There may be a common logic of 
lotion, although not of Observation. 

Definition. 

DEFINITION is a process of generalization, confined in 
to a single property, or a group of properties 

. unity. 

I the first and simplest of the generalizing processes. 
umber of particular things are compared and assimi- 
Bingle property, as round, white, heavy, pungent, 
notion, whose expression in any way is Defini- 
te notion may be complex, or may express several 
nt, as for example < life ' ; but if these are 
as united or grouped, they are still regarded as 

f generalizing, with a view to the Notion, 

of aspects-Classification, Abstraction 

*on. We assume the last as the reprd 

kon of the whole series. 

■ department that we see the assimilating and 

^ in its simplicity and purity. In the do- 

= d, generalization occurs, but con- 

11 •*« I" made in the sequel to the operatiof 



ANALYSIS. 39 

designated * Analysis •/ and as the process is essentially allied 
to the generalizing of the Notion, a brief explanation is here 
given. 

Analysis is an adjunct and a result of Abstraction. The sepa- 
ration expressed by the term is of two kinds. The first is the 
separation of concrete substances, as in the analysis of a water, 
which separates the saline bodies and impurities contained in 
the water. This is often a very subtle operation, demanding 
extreme knowledge, and delicate manipulation. It is, how- 
ever, an actual separation ; the constituents are laid hold of, 
and exhibited apart. 

The second kind of Analysis is the analysis following on 
Abstraction. It is purely mental : the constituents cannot be 
exhibited apart. When, by abstraction, we can think of the 
distinct properties named weight, liquidity, transparency, 
refracting power, solvent power, we divide, or analyze, in our 
minds, the concrete called water (pure), into separate 
properties, although these cannot subsist in separation. 
Water admits of being classed in many groups ; every classifi- 
cation making what is termed an attribute of water. The 
concrete * water,' is thus a complexity, an aggregate, or a 
compound, of many powers ; and when these are stated 
in separation, the concrete is analyzed, abstractively or men- 
tally, not really. 

Analysis thus grows out of generalization, being merely a 
phase or attribute of it. Every act of classifying or general- 
izing necessarily tends to abstractive separation of this nature. 
When we class a shilling with round bodies, with white . 
bodies, with bodies of a certain diameter, with bodies made of 
silver, with bodies stamped as coin — we analyze the concrete 
shilling into the attributes or abstractions, round, white, size, 
; material constitution, coin. 

In the elimination of causes, or productive agents, which is 
a part of the Inductive problem, a preparatory analysis is 
essential, in order to isolate in the mind the various antecedents 
that are to be tested. When a certain impure water is found 
to produce disease, the water is analyzed in the first instance ; 
and not till the different substances contained in it are found 
out, can we enter on the enquiry what particular ingredient is 
the noxious one. This is to apply concrete analysis. Again, 
when we enquire into the cause of the slaking of quicklime by 
water, we must analyze in our mind the inseparable properties 
of water : we must distinguish its solvent property from its 
chemical affinity, and then proceed to enquire which of these 
3 



DIVISIONS OF LOGIC, 
or of any other properties, is the antecedent in the] 

Induction, 

is the generalization of conjoined proper- 
i aioii of individual instances. 

b in induction, we always deal with a proposition, or 

acts or properties : as opposed to the 

a iiich may consist of a single property. 'Iron takes on 

property/ is a proposition made up of two 

I notions— iron and magnetic property. One of these 

ingly could be denned, but could not be matter for an 

>n. 

stance common to Definition and to Induction is 

!i. A single isolated instance may be a proposi- 

:ij unction, but not an induction. ' This magnet ia 

. ' is not an induction : it fails as being only an 

vulual fact 

part of scientific enquiry consists in arriving at 
generalizations. The notion is useful chiefly 
as the constituent of the inductive proposition. 

Deduction. 

i ion is the application or extension of Indue- 
to new c 

on a general proposition is arrived at, the next operation 

ing it to bear on new instances. By help of the* 

methods, we are satisfied that * iron is a magnetic] 

;' and we apply the proposition, as occasion requires; 

lual specimens of iron. Thus the collective iron of 

les under the sweep of the proposition ; which 

the cause, or a cause, of the earth's magnetism. 

luetive process that has been developed into the 

forms of toe Syi.log: 

vation is not made a part of Lome, the subject 

• under the three heads-Definition, Induction, 

n. There would be no radical inconvenience in ex- 

: the subject in this order, beginning with Definition 

th Deduction. Probably, if Logic were now studied 

me or if the science had followed out its Socratic 

commencomont, ihia would have been regarded as the natural 



ORDER OF TOPICS IN LOGIC. 41 

order. Circumstances, however, have led to the inverted order 
— Deduction, Induction, Definition. Although Aristotle himself 
cultivated all parts of the subject, yet his chief labours were 
concentrated in the Syllogism, and his followers took up this 
department to the total exclusion of Induction, and of Defini- 
tion (as a generalizing process). In the re-introduction of 
these omitted branches, they have been made to follow, and not 
to precede the Syllogism. 

Another reason for the inverted order is the elementary 
character of the formal Deductive process ; it being possible 
to explain that process without alluding to the Inductive 
methods for attaining the general propositions. 

Under every arrangement, a preliminary portion of Logic is 
occupied with the elements or constituents of knowledge — the 
Notion and the Proposition. A full account has to be given of 
all the diverse forms assumed by these elements in the various 
departments of information or science. 



BOOK ! 

NAMES, NOTIONS, AND PROPOSITIONS. 



CHAPTER I. 

KAATES OE TEEMS. 

1. There may be knowledge without Language ; but 
all the truths considered in Logic, are Truths expressed 
in \\\»rds. 

The knowledge that guides the lower animals is unconnected 
with They observe by their senses the things about 

them ; and the observations are remembered in sensible forms. 
The bush that gives shelter, the herbage for food, the animals 
yed upon, are known and sought after, by the sole 
gun* ense impressions. 

Human beings have numerous experiences of the same kind, 

involving the order of nature, withont being connected with 

The child has a large stock of sense knowledge 

can understand and employ language. The skill of 

isists, for the largest part, in associations between 

appearances and movements; to the stone-polisher, 

surface at once suggests the next blow. 

in in a highly intellectual profession, as the Practice of 

unmation of skill requires a large sense 

Dg beyond the scope of language. The 

rom books, everything that can be°expressed 

; but there are delicate shades of diagnosis that no 

stored up, without verbal expression, in 

-'■id the touch. 

, however sufficient for the individual, can 

uly to a very limited degree, and with difficulty, com- 



KNOWLEDGE WITHOUT LANGUAGE. 43 

tnnnicated to others. A sense impression, strictly speaking, 
cannot be directly communicated at all. Indirectly, one 
individual can be of nse to others, by bringing them within 
reach of the objects that they need to know. The old can 
carry the young to food, water, or shelter, in the first instance. 
The instructor in medicine can show the actual cases to the 
pupil. As regards movements, or outward actions, there is the 
power of imitation, largely possessed by human beings, and to 
a small extent by animals. 

Such communication is obviously restricted to personal 
intercourse, and, if not so imparted, is lost. The tact and skill 
of manual arts can be preserved only with the succession of 
living artizans. 

The most signal failure in communication unassisted by 
names, is in the attempt to convey easily our discoveries of 
similarity or resemblance. In order to teach another man the 
similarity detected among a number of scattered things, in the 
point of giving warmth, we should have to direct his attention 
to the objects one after another, that he might feel the like- 
ness by the actual comparison. How immensely superior is 
the instrumentality of the names — sun, fire, animal bodies ! 
By the simple process of connecting each of these names, 
with the common name ' hot/ the discovery is made known 
at once* 

This is the primary fact constituting the value of names in 
general knowledge. A generality is a discovery of likeness, 
and nothing more. Now, the most rapid and ready mode of 
imparting all such discoveries is to apply to them a common 
name. The name ' tree ' designates a feature of community in 
a vast number of things; and the use of the name in connexion 
with all such things makes known the community, the ' one in 
the many ' of the Platonic philosophy. 

The higher operations of Reasoning often bring together 
groups of these generalities. A simple product in multiplica- 
tion — eight times nine makes seventy-two, — contains the fol- 
lowing generalities, — eight, nine, multiple, equality, seven, ten, 
addition, two. Now although these might be severally attain- 
able, by the method of confronting the particulars, yet, without 
names or signs, the union of them in the muliplying operation 
would surpass the power of the strongest intellect. liy sense 
alone, we might see that two rows of three, joined in one, 
would make the row of six ; but we would not at a glance dis- 
cover that seven and eight would make fifteen. 

Thus when truths are expressed in language, they can not 



|4 NAMES OR TERMS. 

only be comm I and discussed ; they can also be united 

Ions, yielding an unlimited fund of den- 
expressed, that knowledge of any 
to the tests and methods of Logic. 

,n of knowledge conveyed in language, 

propounded for belief or disbelief, takes the 

!, in Grammar, a Sentence; in Logic, a Pkoposi- 

A tion mentions two things, and is therefore 

4 two names. 

We iMimut impart, by language, the smallest item of know- 

ithout uttering what is called, in Grammar, a sentence, 

;;iins a noun and verb. A sentence is called, 

-niON; and is said to consist of a Subject 

v. The Subject is the thing spoken about ; the 

the thing said or declared of the subject. The single 

limit's 'John,' 4 sun/ 'wind,' * house/ uttered, each by itself, 

no information ; they constitute neither sentences in 

mi \r, nor propositions in Logic. They need to be com- 

1, in a certain way, with other names. 'John comes/ 

Nin shines,' * the wind is lulled,' 'the house faces the 

— are paces of information, sentences, propositions. They 

ntaiu at least tsvo words ; most of them more than two. 

la everyone of the expressions, we dissect the sense into 

• >ken about, the Subject — 'John/ 'the sun/ 'the 

i,' 4 the house;' and into something said of each subject — 

1 shines/ ' is lulled/ 'faces the sea/ 

We farther remark that any two or more words put to- 

nnt amount to an item of information, a sentence, a 

n— something that can be declared true or false, 

disbelieved:— 4 John tree/ 'sun moon light/ 

tempest/ 'house man street of/— are not°sen- 

ftffinnatkme. There is a peculiarity in the wording 

: all informing sentences. ' Gold yellow/ 

da is meaningless, becomes expressive of 

or information by the help of the word 'is ;' 'gold is 

1 bin word ■ is' binds the two others into a sentence; 

'aking, we call it the verb; logically, it 

of the proposition. 

Sentence in Grammar is divided merely into the 

and Predicate-*^ ' gold/ predicate 

'• ; in Lope, the grammatical predicate is farther 

W into the attnbute of the predicate, 'yellow/ and the 






PARTS OF THE PKOPOSITION. 45 

binding word or copula ' is ; ' the attribute — * yellow' is the 
logical predicate. A proposition in Logic, then, consists of 
subject (gold,) predicate (yellow,) and copula (is.) 

In affirmations containing but two names, the copula is to 
be sought in the form of the verb. ' John speaks,' contains 
a noun and a verb ; and the verb 4 speaks' has, of its own 
nature as a verb, the power of affirming. Neither two nouns, 
'John lawyer,' nor a noun and an adjective 'gold heavy,' 
would give any knowledge without a third word as copula ; 
but we have many propositions where a noun and a verb (in 
a single word) contain a complete affirmation, * baby walks, 
1 food nourishes,' ' Sirius twinkles.' 

In these last forms, we can distinguish subject and predi- 
cate by our grammatical knowledge ; the noun is subject, 
the verb is the grammatical predicate, and unites in itself the 
logical predicate and the logical copula of affirmation. Also 
in such forms as ' gold is heavy,' we are guided by grammar. 
We know that an adjective, as ' heavy,' is never a subject, and 
must therefore be the predicate. The noun can be both a 
subject and a logical predicate ; — ' gold is a metal,' ' Caosar is 
emperor' contain each two nouns, one being subject and the 
other predicate ; which is which may be usually determined 
in English by the order ; the subject being given first. When 
the order is inverted for Rhetorical effect, we must judge by 
the meaning and the context. 

The fact cannot be too soon laid to heart, that the predicate 
is usual ly^jarg^m meaning than the subject ; it applies to 
many other things besides the one spoken of at the time. 
' Gold is heavy,' but not the only heavy thing ; ' heavy' ap- 
plies to other substances besides gold. ' Woody fibre is not 
fit to eat,' leaves us free to affirm that there are many things not 
fit to eat, as well as woody fibre. Hence, subject and predi- i\ 
cate' in affirmation, are not necessarily co-extensive ; in point of J 
fact, they are very seldom co-extensive. 

3 There are various motives or reasons for commencing 
Logic with an examination of Names. 

(1). It has now been seen that a Proposition, the final con- 
stituent of Logic, the logical form of all knowledge, is made 
up .of Names. The characters of propositions, therefore, can- 
not be given without referring to their component names. 

(2). In the use of Names are involved numerous sources of 
error, — pitfalls and snares ; and it is one function of Logic to 
give warning of these. 



|Q NAMES OK TERMS. 

urination of the existing vocabularies of mankind 
; Bt ie to the universe of existing things. A 

If fully developed, indicates all the things that the 
, .peaking it have taken notice of; these may or may * 
ting that the world contains, but they are every-: 
to light by the combined observation of many 
Im . u | s. Now, it is found useful, in laying 

niu of a comprehensive Logic,— a code of Evi- 
tfethocU for all kinds of knowledge— to survey 
beads the whole universe of ascertained things. 
of the most advanced and cultivated people, 
or of Bei era! peoples combined, is the best available aid to this I 
operation) 

In an advanced language, we find names for the heavenly 
and their revolutions, and changes; names for large 
objects on the earth — sea, mountain, river, &c. ; names for 
■.•material substances — water, stone, iron, gold, wood, 
names for powers and forces, — wind, weight, heat; 
names for living bodies — plants and animals; names for the 
iily parts and functions of human beings ; names for men- 
tal functions — pleasure, pain, will, thought; names for the 
social facts of humanity — king, law, punishment, property, 
me | names for the numerous exercises and functions of 
mankind — husbandry, trade ; and so on. Now the names give 
the clue to the various objects named. Again, we have names 
I forms of speech indicating agreement among things — 
eric or common words, as star, solid, heat, power, pleasure 
— which show us that natural facts frequently recur. Farther 
we have names that imply other names ; — ruler-subject ; 
up-down ; whence we learn that the world contains mutually 
1 things. 

4. A name is defined, in the first instance, 'a mark at- 

to a thing to enable it to be spoken about/ 

In giving names to objects, the end primarily sought is 

t ion and discourse. Once invented, names have 

the additional function of aiding the solitary thinker, in re- 

Bldog, and arranging his thoughts. 

larked by Mr. Mill, as a corrective to the unguarded 

ke and others, that names are the names of Things, 

I of the Ideas of things. The word ' sun ' is the mark of the 

by that word, and not simply the name of our thought 

i. To suppose that names are names of ideas alone is a 

m, confounding together the object and the sub- 

Y ft, The Thing itself (if an object) is determined by our sensa- 



SINGULAR AND GENERAL NAMES. 47 

tions, or what we call our experience of actuality ; the Idea is 
purely subjective; it is a mental element strictly so called. 

5. For the purposes of Logic, Names have regard to 
Generality and to Relativity ; in correspondence with 
the two foundations of knowledge — Agreement and Differ- 
ence. 

Names may be variously classified. They may be divided 
phihlogically into languages, as English, French, Hebrew. 
They may be divided for rhetorical purposes into plain and 
figurative ; the figurative class containing species — Hyperbole, 
Irony, &c, — Opposed to Logic, as departing from truth for 
the sake of the feelings. 

There is also a division of Names under grammar, namely, the 
Parts of Speech, which may be looked upon as in great part a logical 
division. Thus, the Noun may be always the subject of a proposition, 
and is often a predicate. The Adjective has two logical functions ; 
— it may be, and frequently is, a predicate ; and, secondly, it is the 
specifying designation of a genus . expressed by a noun ; man 
(Noun), genus, white (Adjective) man, species. The Verb has the 
important logical function of affirmation or predication ; there can 
be no proposition without a verb ; i fire hums,' * honey is sweet/ 
The remaining parts of speech possess no logical function. 

NAMES CLASSED ACCORDING TO GENERALITY. 

6. In classing Names, y^ith reference to Generality (or 
Agreement), the fundamental distinction is between Singu- 
lar Names and General Names,* 

The process of generalization, through the tracing of agree- 
ment, is a thoroughly scientific or logical process. Now, 
whether for a general notion (as ' liquid '), or for a general 
proposition (' liquids find their level '), the names employed are 

* In the foundations of knowledge, Discrimination or Relativity may be 
supposed to have the priority ; we discriminate first, and trace agreements 
in difference afterwards. On this view, the classification by Relativity 
might properly precede the classification by generality. In reality, how- 
ever, we cannot treat either without the other being implicated ; the 
relative couple, light-dark, is understood by us only as generalized 
upon many recurrences of the transition : we do not go back, for our 
typical notion of the phenomenon, to the first occasion when we experi- 
enced the shock of transition, or before we had identified several recurring 
shocks. There is, therefore, no special disadvantage in beginning with 
generality: we being aware that there could be no notion of either 
individual or general, without prior shocks of discrimination or relativity. 
Whichever of the two facts is under consideration, the other must be 
tacitly supposed. 



U ACCORDING TO GENERALITY. 

general names. I r, the individuals that have to be 

nnd cnm|.:iml in order to the generals, must also have 

llriduals,— ' the Rhine,' 'the Caspian sea.' 

or Individual Name is a name applicable 

i sral Name is applicable to a number 

I their being similar, or having some- 

:non. 

»phalu§, Sirius, Teneriffe, the Alps, England, 
.Dame, Koh-i-noor, are Singular names; they 
i &ch one individual object. 

r, mountain, kingdom, city, building, gem, 

is ; they apply each to an indefinite number 

of things having a certain likeness or community among 

Name may be of various forms. One form, 

exhibited in the above examples, is a single meaningless mark 

or designation appropriated to the thing. ' Xerxes/ 'Sirius' 

function but what might be served by any other 

re utterance applied to the objects indicated. A 

i on of this form is seen in the many-worded designa- 

of individual men and women, John Davidson Ross; 

ne Louisa Brown; David Smith, of George Street, 

V plurality of words must be resorted to, because 

Maria, IJmwn, &c, are used in naming a great many 

luals, and are therefore not distinctive. Such names 

furnish the least possible information about the persons named. 

ssarily indicate human beings*; horses, dogs, 

vive designations from the same class of words. 

form of the singular name is seen in such examples 

ing Pope,' • Her Britannic Majesty's minister at 

verer of America,' 4 the high-priest of Baal/ 

I of the family,' « the pinnacle of Europe,' ' the 

These are severally applicable to individuals, 

previous generalities, combined so as to 

r meaning to deBnite individuals. They are signifi- 

i Bingular ; and the significance grows out of 

aames, as nation, array, multitude, assembly, 

angular ; they are plurality combined into unity. 

™ch as there are many nations, armies, assemblies, 

■eral. There being but one < universe/ 

and Bingular 

Names of Material-earth, stone, salt, mercury, water, 



CONNOTATIVE NAMES. 49 

flame, — are singular. They each denote the entire collection' 
of one species of material. If Space and Time be not regarded 
as abstractions, they fall under the present class. 

8. General Names are said to be Connotative ; that is, 
they denote objects, and connote or imply attributes, or 
points of community among objects. 

As a mere mark, a name has no power beyond simply denot- 
ing, or pointing out its object ; Sirius suggests the star of 
that name ; London has no other function than to make us 
think of the object named. But the general name, the result 
of assimilation, denotes the individuals, and connotes or im- 
plies a certain similarity among them, in other words, a com- 
mon attribute. The word ' star' denotes any star in the firma- 
ment, and implies or connotes the similarity pervading the 
stars ; the word ' metropolis ' is the name denoting London, 
Paris, Berlin, and also declaring that all these separate objects 
have points of resemblance ; the resemblance is the common 
attribute of the things, and the connotation of the general name. 

All Class names, therefore, being general names, are conno- 
tative names : — man, animal, plant, tree, metal, mountain, sea, 
kingdom, government, factory, circle, virtue. 

Besides, the general or class nouns, Adjectives are to be held 
as connotative : — for example, white, square, wise, virtuous. 
These are generalized names ; they are given to a plurality of 
things agreeing in a certain way. They each denote particular 
objects (the noun being supplied) ; they connote or imply a 
community in these objects. They are significant and not 
meaningless names. 

Adjectives are obviously products of the generalizing process 
no less than class nouns. The same generalization is often ex- 
pressed both as a noun and as an adjective, — circle, round or 
circular ; colour, coloured ; weight, weighty. 

The limitation to this practice belongs to the nature of the things. 
The function of an adjective is to narrow the application, and 
increase the meaning of a noun ; * wise men' are fewer in number, 
and more numerous in attributes than men. Now, in order that a 
noun may take on the whole meaning of an adjective, that mean- 
ing must be a limited one ; it must be expressive of only one or a 
few attributes. ' Men ' can take the qualifications signified by the 
adjectives 'wise,' 'old,' 'tall,' 'virtuous.' If, however, we were 
to coin an adjective from the class ' horse,' there are no objects 
in nature that could take, in addition to their own attributes, all 
those possessed by horses. When adjectives are formed from such 
classes — commonly called natural kinds — they are used only in a 
select or partial meaning. ' Golden ' means either made of gold,, 



(j0 NAMES OR TERMS. 

or poewring the salient and striking attribute of gold ; <feli: 
atuie of the genus ' f el ; human is son 

reneral name is explained as being the nar 

the name of the class men. Bat the wor 

-the class definite, and the class in- 

inite is an enumeration of actual iudi- 

of the Realm, the Oceans of the globe, 

The individuals of these classes have a 

certain h common character; while, in addition to 

q all known and enumerated. The question 

bain object belongs to the class, might be settled 

. by its possessing the class likeness, secondly, 

rand in the enumeration. The shortest way of 

ascertaining whether a given person is a peer of the realm 

>ok for his name in the Peerage. At all events, 

with the method of judging by means of class 

lea. 

The class indefinite is unenumerated : — such classes are 

. <^old-bcaring rocks, men, poets, virtuous. These 

mtain individuals known and many more unknown. 

complete list whereby to test any supposed indi- 

J. The sole criterion is the class attribute or likeness. 

her a newly-discovered heavenly body be a star or a planet 

is to be decided by finding its characters. If it is a fixed body, 

th stars, if it circles round a fixed? star, we class 

it wi;h plan- 

icceptation of the word, class name and general 

■ identical. The class name denotes an indefinite 

number of individuals, and connotes the points of community 

The general name does the very same thing. 

n ' wise men' is a class name and also a general 

o the acceptation of an enumerated and finished 

name is not the same as the general name; it 

an additional, and exceptional test of the claims of 

to belong to the class. ' Thales is one of the 

n f exemplifies the class definite; 'Socrates is 

h the class indefinite, known only by the mean- 

al name. J 

t designated by the words 'denote' and 
>ponds to Hamilton's distinction between 
qiU »« and quantity in Comprehension. 

The deuotutiou of a general term, the individuals that it 



EXTENSION AND COMPREHENSION. 51 

applies to, is designated by Hamilton, its Extension, or extent. 
The denotation or Extension of the term 4 man ' is the whole 
population of human beings. The connotation or Compre- 
hension is the community of attributes, or points of agreement, 
making up the characters, marks, or definition of men — animal 
life, anatomical peculiarites, mental endowments, &c. 

The two facts — denotation or extension, and connotation or 
comprehension — are reciprocally opposed ; the greater the one 
the less the other. The term ' animal ' has a greater denota- 
tion or extension than the term ' man ; ' it includes all men, 
and the population of brutes besides. It has so much the less 
connotation, or comprehension ; it connotes only the points 
common to animals, which are much fewer than the points 
common to men ; — animal life in general, without distinctive 
organized forms. On the other hand, the term 'wise men' 
denotes less, has less extent, than the term men ; it applies 
only to a selection of men. It connotes or comprehends all 
the more ; to the connotation of men it adds the attribute con- 
noted by ' wise.' 

Mr. De Morgan has dwelt at great length, and expressed in a 
variety of forms, the distinction between Extension and Compre- 
hension — Breadth and Depth, — and has followed it out, like 
Hamilton, into syllogistic" forms. 

He remarks that Terms are used in four different senses. Two 
of these, he calls objective, as directed to the external object. The 
first are terms expressing an individual standing alone, or out of 
all connexion or relationship with any other individual ; as John, 
man. The second, the name of an individual quality, forming part 
of, or residing in, the individual object, as the term ( human,' or as 
'animal,' when applied to man. The author considers that the 
ordinary syllogism has reference to these terms, which he calls 
terms 4 of the first intention,' and also arithmetical. The usual 
form of a proposition is to declare some objects to be included in, 
or to be excluded from, some other objects; or to affirm or deny 
of them some quality in the form now stated — ' men are animals,' 
4 kings are human.' 

The two other senses of Terms are called by the author subjective. 
The first is to represent a class, or collection of individuals, named 
after a quality common to all : these are Mill's connotative class 
names. The second represents the attribute of the class apart, in 
other words, the abstraction as conveyed by the abstract name. 
In short, in these subjective meanings, explicit notice is taken of 
the fact of 'generality' or 'generalization;' the one in the 
concrete and the other in the abstract designation. 

It may be remarked on the distinction between these objective 
and subjective meanings, that it hardly involves any serious 
difference. Unless the objective terms were confined to proper 



\MES OR TERMS. . 

ro forms having generality, and that generality 

1 nought into the ioreground) is all that is 

ihji-ctivo terms for class and attribute, lake 

of all the four— man, human, mankind, 

objective, the two second subjective ; the 

• man ' and ' mankind ' is impalpable ; while 

merely the abstract noun of the adjective human.' 

distinction is between the class and the class attribute. 

tension ami comprehension,' Mr. De Morgan employs 

and 'intent,' also ' scope' and ' force. 1 He 

-t ion to an important distinction in the modes 

of extension and terms of comprehension res- 

Y. : terms of extension are combined, as ' man' and 

an arithmetical summation of individuals ; this he 

When two terms expressing attributes combine, 

1 • polished, 1 it is not an arithmetical sum or 

, but a joint inherence of quality in a common subject; 

lie name composition. He remarks that we have 

i English designation for the separate parts of a coni- 

thifl last sense. The word 'part' refers to extension: 

nstitucnt ' and ' element ' are a nearer approach to 

the Idea, ^ at do not exactly hit it. 

Bystein, expresses aggregation by the sign of 
addition, man + brute, x-f y; and composition by a product, 
X polished, x y ; and conducts his manipulation throughout 
. it y with these suppositions. 

The final result of the generalizing process is the 

A31E. This is an elliptical form of speech, 

-Tul, but also greatly abused. 

Su lotion, weight, breadth, roundness, white- 

-weetuess, roughness, polarity, wisdom, justice, 

died abstract names, as signifying qualities or 

a without reference to the things that possess the 

They seem to separate the points of community of 

rts, frem the objects themselves, an operation 

, and even in thought, but supposed, by a 

n, to be possible. 'They give the meaning ex- 

nnotation of the corresponding class desig- 

t bin «s, heavy things, broad, round, white, 

i) entirely the denotation. 

■ name, although occurring in all languages, is 

[wired tor ordinary speech ; nor indeed for 

meaning to be conveyed can always be Riven, 

althoogh not so shortly, by means of general or class names. 

e motion expresses what is meant by 'moving 

ffect of it is to limit the consideration 



ABSTRACT NAMES. 53 

to this one feature of the things in qnestion ; it amounts to 
saying * moving things in so far as moving/ or with reference 
to the one circumstance common to them all, and not to any 
other circumstance that may attach to particular individuals. 
So * justice ' expresses the same meaning as 'just actions ; ' 
the only existing fact corresponding to the term is the class 
'jusfc actions.' There is no such thing in the universe as 
justice by itself ; we cannot point to a disembodied justice. 
The term signifies 'just actions,' with a peculiar stress or 
emphasis put upon the features of agreement ; 'just actions in 
so far as just, or viewed solely with reference to their being 
just. 1 The proposition 'Justice commands respect, 1 is the same 
proposition as 'just persons are respected persons,' with a 
more emphatic indication than the class names seem to give, 
that the causation refers solely to the points common to 'just 
persons,' and to 'respected persons.' ' Just persons so far as 
just are respected persons so far as respected.' 4 Beauty gives 
pleasure ' is equal to ' beautiful things (in so far as beautiful) 
are things pleasant (in so far as pleasant).' There is no 
4 beauty ' in the abstract giving ' pleasure ' in the abstract ; 
such a supposition is the old error of Realism, scarcely yet ex- 
tinct. 'Mind is the cause of force' can mean only 'beings 
possessing mind, in so far as possessing mind, are the cause of 
moving things considered as moving.' 'Mind' is inseparable 
from certain actual beings called persons, beings mentally en- 
dowed, &c. ; and ' force ' is an abbreviation for moving things, 
the cause of other moving things, in so far as moving. 

A great power of abbreviation is given by abstract terms, 
which is probably the motive for introducing them so largely 
into common speech. This is apparent from the circumlocu- 
tions necessary for avoiding them. 

The abuse of abstract names is exemplified in the almost 
irresistible tendency they have to suggest the existence of 
things in the abstract. We are led to suppose from the use 
of the terms Time, Space, Mind, that there is something in 
nature called Time, apart from things enduring ; something 
in Space different from things extended and the free move- 
ments of extended things ; something named Mind, distinct 
from beings exerting mental functions. 

An important logical exercise, for detecting the fallacies 
nursed under abstract names, is to translate abstract proposi- 
tions into the equivalent propositions made up of general 
names, not abstract.* 

* * If the student of philosophy would always, or at least in cases of 
importance, adopt the iuu of throwing the abstract language in which it 



64 NAMES OR TERMS. 



Jn contrast to abstract names, all general names, or class 

i e names : they express the agree- 

. not as an impossible detached fact, 

v of the case, namely, as the things that 

ment. All class nouns, as man, tree, star, 

s brave, tall, lustrous, — are concrete general 

i?e name is thus a concrete name. 

»t confound, as is sometimes done, a general 

abstract name. A general name is opposed to 

rviJual or singular name; an abstract name is opposed 

Dame, whether general or individual. Tbo 

rhitenew' is opposed to the general designation 

,' and through it to every particular white thing; 

name cannot possess the double function of the 

denoting a thing and connoting the similarity 

iy be said, as by Mr. Mill, to denote the simi- 

or tho common attribute, and to connote nothing 

however, nothing gained, anvwhere in Loo-ic, by such 

nation. The Abstract name is the last°product of 

ion; alike the facility and the snare of general 

on. & 

, ll ' nce of the generalizing process that there 

s of lower and higher generality, as English- 

European, man, animal, organized being ; circle, curve 

figure, extended thing. These luccessiye geneS 

great part in science, and lead to many technical 

"bona which have to be considered in Logic fbnt their 

> place is in the following chapter, on the Notion or 

•nd group of Names, viewed for Logical ends 
s th« ise connected with Relativity 

, know ' V m lan S ua # e - K everything 

inence ^^^ W something 

Lave a double mearint or ill t ^^ 

-0 names Wo Snnofh-fK 617 "^ ° g 

* - F~* out o^d^t^S 

t pies f™ ^v? tW °, f the immense mass 0{ 
ii. p. 159.) P f ° r ^''osopby-' (Bailey's Letter* 



POSITIVE AND NEGATIVE NAMES. 55 

conscious in a particular way by passing from light to dark, 
and from dark to light The name ' light ' has no meaning 
without what is implied in the name 'dark.' We distinguish 
the two opposite transitions, light to dark, and dark to light, 
and this distinction is the only difference of meaning in the 
two terms ; ' light ' is emergence from dark ; * dark ' is emer- 
gence from light. Now, the doubleness of transition is likely 
to occasion double names being given all through the universe 
of things; languages should be made up, not of individual 
names, but of couples of names. When we refer to the actual 
case, we find a very great prevalence of couples, but we can 
hardly call it universal. We have such instances as heat-cold, 
motion-rest, up-down, light-heavy, thick-thin, hard-soft, rich- 
poor, life-death, parent-child, ruler-subject ; and we must en- 
quire how far the system extends, and, if short of universality, 
why it is so. 

12. The great distinction of Names founded on Rela- 
tivity is expressed by Positive and Negative names. 

No one designation exactly suits the principle of universal rela- 
tivity. The couple ' Positive and Negative' is the best we have, but 
the term 'negative' inclines too much to the idea of deficiency, or ab- 
sence of a quality, without the presence of a corresponding opposite. 
Now the negative of a real quality is as much real as the positive ; 
North and South, have an equally good title to positive existence. 
Heat and cold, or the transitions cold-heat, and heat-cold, are 
equally real or present experiences. 

The terms ' Relative ' and ' Correlative ' are also too limited for 
the purpose ; they are too much confined to complex relationships, 
as, parent-child, teacher-scholar, mover-moved. 

Of these two couples, the one most easily adapted to the univer- 
sality of relation is the first — ' Positive and Negative ; ' which we 
shall adopt with the understanding that ' negative ' has always a 
real existence, no less than ' positive.' So explained, it may be 
stretched to the whole length of universal relativity. Under 
* Relative ' and ' Correlative,' will be explained certain special rela- 
tionships, growing out of the complicated arrangements of the 
world. 

Mr. Mill expresses the nature of Positive and Negative in 
the following terms : — ' To every positive concrete name, a 
corresponding negative one might be framed. After giving a 
name to any one thing, we might create a second name which 
should be a name of all things whatever, except that parti- 
cular thing or things. These negative names are employed 
whenever we have occasion to speak collectively of all things 
other than some thing or class of things. Thus not-white de- 



66 NAMES OR TERMS. 

notes nil things whatever except white things ; and connotes 
th essing whiteness/ ' Names which are 

are often negative in reality, and others are 
»ngh their form is negative. The word in- 
sample, does not express the mere absence of 
expresses a positive attribute, that of being 
in fort or annoyance. So the word unpleasant, 
notwithstanding its negative form, does not connote the mere 
<v of pleasantness, but a less degree of what is signified 
bj the word 'painful, which is positive. Idle on the other hand, 
is a word which, though positive in form, expresses nothing 
n hat would be signified either by the phrase not working, or 
B not disposed to work; and sober, either by not 
h, or not drunken.* 
Thus Far Mr. Mill. Mr. de Morgan carries the distinction to 
ength of a mode of universal relativity. He says : — * Let us 
■ pair of contrary names, as man and not-man. It is plain 
that between them they represent everything imaginable, or 
rial, in the universe. But the contraries of common language 
iiMiallv embrace, not the whole universe, but someone general 
'1 has, of men, Briton and alien are contraries : every man 
be one of the two, no man can be both. Not-Briton and 
identical names, and so are not-alien and Briton. The 
may be said of integer and fraction among numbers, peer 
commoner among subjects of the realm, male and female 
R animals, and so on. In order to express this, let us say 
that the whole idea under consideration is the universe (mean- 
merely the whole of which we are considering the parts) 
and let names that have nothing in common, but which be- 
ll them contain the whole idea under consideration, be 
I contraries in, or with respect to, that universe. Thus the 
being mankind, Briton and alien are contraries, as 
'laier and civilian, male and female, &c. ; the universe 
- animal, man and brute are contraries, &c.' 

•Morgan here supplies what is requisite to the pre- 

Q of Positive and Negative. It is not strictly 

that 'not-white' means everything in nature 

things; a more limited universe is supposed at 

»*. Probably the universe 'colour;' and the meaning of 

bite is black, red, green, yellow, blue, &c. Sometimes a 

hi- ,L Mn i ,, : i nni y er f e ™y be intended, the universe of white, 

cli h ,V ^t^** of grey; the prismatic colours being ex- 

dnded ; in which case not-white means black and grey. 

<>™ a term is ambiguous, one mode of rendering it pre- 



UNIVEKSB OF THE PROPOSITION. 57 

cise, is to name the opposite of what is meant. The term 
1 civil ' has many meanings ; ifc is opposed to natural, to 
militar} r , to ecclesiastical, to uncivil or discourteous, and so on. 
The same purpose is served by stating what higher universe is 
present to the mind of the speaker. If the universe be the 
condition of human beings in relation to one another, * civil ' 
means organized into human society ; if the universe be the 
departments of government, ' civil ' is known to exclude 
military and ecclesiastical ; if the universe be manners or ad- 
dress, civil is understood in that connexion. 

Thus of the three things — the universe or genus of the 
speaker, the positive, and the negative — we cannot know one 
without knowing the others. Any ambiguity in one is reme- 
died by stating a second ; it matters not whether that second 
be the contrary or the entire universe. In common speech, 
we are usually able to assign the universe from the context or 
occasion. In discussing the origin of human society, we see 
that the words ' civil ' and ' natural ' are employed to divide 
the universe of man's condition in respect of society. When 
we do not know the subject of discourse, we are still made 
aware of what a term means, if the opposite happens to be given, 
as 'civil,' * not rude.' 

13. In those cases, where a universe contains but two 
members, the one is the complete negative of the other. 
This is the most marked form of contrariety. 

Heat-cold, light-dark, high-low, straight-jbent, good-evil, 
pleasure- pain, virtue- vice, health-disease, man-brute, are com- 
plete and emphatic contraries ; the negative of one member is 
the affirmation of the other ; the affirmation of one, the nega- 
tive of the other. [ aJLc yj ( ^ ^ 

14. When a universe, or higher genus, contains many 
members, the contrariety, although no less real, becomes 
diffused. 

* Red ' in the universe colour is not negatived by any single 
colour, but by a plurality of colours. If we are dividing 
colours according to the Newtonian spectrum, 'not- red' means 
six colours. In a full enumeration of shades of colour, ' not- 
red' would be a list of many scores of individuals. The 
contrariety is then diffused and pointless. ' Not an English- 
man ' leaves us in a wide sea of possibilities ; the universe 
being natives of different countries. 



H NAMES OR TEEMS. 

contains various modes of expressing 
gatrou. 




language contains percmp* r « "»"^ - 

P y names: young-old wise-foolish, brave- 

.-falling, good-evil, sweet-bitter, rough-smooth, 

o certain general modes of stating negation. 
the prefix not :— not-cold, not-well, not a fish, 
letal, non-electric. 
The prefixes 'un,' 'in,' and the suffix Mess, are also used: ] 
unknown, incomprehensible ; heedless, blameless. 

6 is also served by various circumlocutions — 

but,' ' all but,' ' all that remains when one is 

:i~' These last forms express accurately the real 

: negation when disguised by plurality of contraries; 

a universe is assumed, the given positive is subtracted from 

thai universe, and what remains is the negative or opposite. 

4 All the simple bodies except the metals ' explains the meaning 

of not-metal, in the universe * simple body.' ' All the parts of 

h except the noun,' is the full rendering of 'not a noun/ 

;n.' 

gative of a real property or thing is also real. 

If a negation be simply the remainder when one thing is 

subtracted from a universe containing more than one, such 

ion is no less a positive reality than the so-called positive. 

In fact, positive and negative must always be ready to change 

\e wp, negative down; positive down, negative 

ertain circumstances, where one side seems to be 
by a special propriety ; as when we express fullness, 




thing-nothing,' — these seem to give us on the one 

positive conception, on the other side, a truly 

the reversal of the terms would seem harsh, un- 

rted. Yet, in all such cases, the negation is a 

able phenomenon ; a genuine experience of the 

, although, in most instances, a less agreeable 

». The position of being in deht is a real fact or 



THE HIGHEST UNIVERSE. 69 

state, with characteristic features ; there is an assignable uni- 
verse, the universe of pecuniary circumstances ; we subtract 
from that total the cases called being ' out of debt,' * solvent/ 
and we find as a remainder cases of ' being in debt ;' the two are 
mutually opposed ; we might call either positive, and the other 
;ve. Any awkwardness in the free transposition of the 
epithets arises from the imperfection already noticed as 
attaching to those epithets, considered as names for universal 
relativity. They are frequently used with more limited and 
special associations, such as to give a greater seeming pro- 
priety to the employment of ' positive ' for the conditions ex- 
pressed by abundance, wealth, credit, strong, pleasurable, 
good, than to the employment of * negative ' for those condi- 
tiuns. 

The highest universe of all must contain at least two things, 
mutually explaining, and equally real. This remark is neces- 
sary, because a fallacy is often committed by using the forms 
of language where there is no longer a reality to correspond. 
Thus matter-mind, or more correctly extended-unextended, 
— object-subject — signify a real couple, mutually explaining. 
The denial of matter, extension, or the object- world, is the 
affirmation of mind, the subject-world. Up to this point, we 
are in the region of real and actual experience. There is a 
transition familiar to us, between certain states of conciousness 
called matter, and other states called mind : we know both, 
by mutual contrast ; while our knowledge can ascend no 
higher. Still, language can take a flight beyond. We can 
in words, sum these two facts together — mind and matter, 
subject and object ; we can even use a single term as the 
equivalent of this sum — Universe, Existence, Absolute ; but our 
knowledge is not advanced by the step. There is nothing 
correlative to the supposed universe, existence, the absolute ; 
nothing affirmed, when the supposed entity is denied. Matter 
we can conceive, because of its real opposite, mind ; but ' exist- 
ence ' has no real opposite. 

Granting for a moment, that there were such a thing as 
non-existence, to give reality to existence, what is to prevent 
us from summing these two together, giving a name to the 
Bum, and insisting on the reality of this new entity, with a 
correlative reality ; and so on withoutend ? Wemust obviously 
stop somewhere ; and the proper point is the highest couple 
that generalization can carry us to. This is to conform to the 
essential relativity or doubleness of knowledge. An absolute 
unity is not knowledge, but an unmeaning phrase. 



g KAMES OR TERMS. 

r iai Relationships, apart from universal 

I in the processes of nature, and in 
hips of living beings. From these, we have 
mis. 

[ n f communicating motion, there is a thing moving 

>ved, something striking, and something 

support, there is a supporter and a thing sup- 

braction and repulsion require two things; the 

g and the attracted. Heat and light emanate from 

v and operate upon other bodies. Acid is relative 

, both to a neutral salt. 
limi implicates parents and offspring. Male is cor- 
with female; the name 'male' has no meaning by 
b must understand ' male ' and 'female ' by the same 
i m li\ t of intelligence. The fact that they express is a 

com] ; both parties are concerned in it; the part of 

cannot be separated from the part of the other. 
* Luck ' and 4 key ' are correlative terms of this kind. We 
not understand or explain a key without the mention of a 
lock, nor a lock without a key. 

The complex structuro of human society contains many 
situations, where two parties mutually enter. Such are sove- 
reign-subject, master-servant, buyer-seller, debtor- creditor, acc- 
used, teacher-pupil, doctor-patient, churchman-dissen- 
lese are cases, not of universal, but of special, relativity, 
and deserve to be considered apart from the more fundamental 
ips inherent in knowledge. 
All active verbs are correlative from the very necessity of 
.structure. An agent supposes something to act upon ; 
tmh 1 in act, it has no meaning. A conqueror that 

r conquered anybody is an absurdity. 

mmonly said, with reference to the great problem 
•ion of a Material World, that knowledge 'sup- 
B a mind knowing, and a thing known'; which is inter- 
ring that there is a mind apart from matter. In 
proves only, that, in the act of knowledge, 
her act, there is a mutual participation of two 
r these things can exist as separate, detached, 
and lent entities, is a distinct enquiry. 

aning of every object of knowledge enlarges 
Ittrgement of its negatives or contraries. 
Id, 1 in the universe 'simple body' means the opposite. 



^-irinm^y 



RELATIVITY UNIVERSAL. 61 

or exclusion of the other sixty-two simple bodies. If ten more 
elements be discovered, there will be ten more exclusions or 
opposites. ' Health' to a rustic means the absence of a certain 
number of familiar diseases — catarrh, rheumatism, dyspepsia, 
measles, &c. ; to a hospital nurse, it has a still wider meaning ; 
to an institutional writer on Medicine, it means the exclusion 
of upwards of a thousand diseases. 

There is no escape from the principle of universal relativity. 
There is no possibility of mentioning a thing, so as to be 
intelligible, without implicating some other thing or things, 
equally intelligible. One might suppose that a chair is an 
absolute and unconnected fact, not involving any opposite, 
contrary, or correlative fact. The case is quite otherwise. 
The chair is immediately opposed to vacuity, and to the 
physical and mental condition of the person suffering from its 
absence. It may, according to the circumstances, have a still 
greater compass of opposition, and so a still wider meaning ; 
it may be opposed to a table, a bed, a footstool. It may have 
still farther oppositions ; the reference may be to the universe 
| seat '; in which it would be opposed to a ' stool/ * a bench/ 
a 'sofa/ 'an ottoman/ &c. The full meaning would then be 
I do not want a * stool/ ' sofa/ &c, but a chair. 



CHAPTER n. 
CLASSES, NOTIONS, OR CONCEPTS, 

1. These designations signify generalization applied to 
single properties, or to groups of properties regarded as 
units or wholes. 

The contrast is to Propositions, which are generalized 
couples, with the affirmation (or denial) of coincidence. 

We may identify and generalize a number of things under 
a single point of community, as ' round/ ' heat/ 4 polarity.' 
In the concrete, these generalities are named classes — * round 
things/ ' hot things/ ' polar things.' When the point of com- 
munity is spoken of in the abstract, — Soundness,' 'heat/ 



62 5, .NOTIONS, OR CONCEPTS. 

Ion is called a general notion, a general 

:, simply a notion, or concept; the terms 

b' being regarded as more applicable to 

. t liiui to a single concrete object. The 

an equivalent expression, for the 

ible to confound these classes, or notions, having 

; uro in common, with propositions, which 

(wo tilings. But many classes have more 

ire in common; as 'metals,' which agree in four 

ie class * man ' has a still greater number of 

ment. In such instances, the distinction between 

ie general notion, and the proposition, appears 

av with. It no longer turns upon the number 

d proj cities, but upon the manner of expressing their 

conjunctions. In the class, the conjunction of the properties 

in a group is assumed; there is no question raised, as to 

unjoined. In the proposition, this is treated 

bo doubt, and the doubt is met by a positive assurance, 

in of a distinct affirmation, backed up, if need be, by 

evidence. 

ing are examples of the generalized Proposition, 
involving two notions linked together by affirmation (or dis- 
denial). * The circle contains the largest area within 
inference ' ; ' heat is convertible into mechanical 
metals are the bases of salts.' In every one of 
re are two distinct general classes or notions ; the class 
with the class or notion * largest area in a given 
Pence'; the class or notion 'heat' and the notion 
ible into mechanical force ' ; the class * metals ', and 
( salts.' But the existence of two notions 
does not exhaust the force of the proposition. There is farther 
nation that the two in each case do, or do not, go to- 
nearer is supposed to be in ignorance or in doubt as 
t the notions 'circle' and * maximum of area ' are 
«d the proposition sets this doubt at rest, so far 
n can go. 

only the affirmative or conjunctive proposi- 

be confounded with the double-propertied 

he negative proposition declares the disjunction of 

of the Class, Notion, or Concept, has been 
?bt out under 'Names,' and more especially 
anded on generality. 



ONE OR MANY CLASS FEATURES. 63 

2. Many classes are based on a single point of com- 
munity ; otherwise expressed by saying that they possess 
mly one attribute ; as white, hard, long, extended, round, 
)olar, hot, pleasure, multitude. 

4 White,' being a single, indivisible impression on the mind, 
be things that agree in it, and in nothing besides, are classes 
msed on one point of community ; they have only a single class 
attribute. Such classes are numerous. The properties — 
:ransparent, hard, soft, elastic, brittle, long, square, hot, liquid, 
lir, simple body, pleasing, just, powerful — are single features of 
igreement ; there are communities of things comprising 
hese several individual features, and no others ; and they are 
ill treated as simple effects. * 

3. There are classes formed upon more than one, but 
ret not many, points of community. 

A good number of classes have two points in common. A 
louse is (1) an artificial erection, (2) for the purpose of shel- 
ving living beings or things belonging to them. A town is 
1) an assemblage of inhabited buildings, (2) under a common 
government. A magnet is a body (1) attracting iron, and (2) 
Dolarized. 

As an example of a triple-propertied class, we may cite 
Mind,' which comprises three distinguishable functions- — Feei- 
ng, Will, Intellect. Chemical Affinity has also a triple defini- 
:ion ; — definite proportions, change of properties, production of 
leat. 

The long received definition of * Inflammation ' enumerates 
'our properties — Heat, Redness, Swelling, Pain. 

4 There are certain Classes grounded upon a large and 
ndefinite number of common features. These are termed, 
jy pre-eminence, real Kinds, Injimce Species, lowest Kinds. 

* The singleness, in some of these instances, is relative to the usual mode 
:>f defining by reference to a higher genus with a statement of the specific 
lifference (per genus tt differentiamj . Thus 4 round ' is a plane figure with 
i special mark (given in the definition of the circle). The inclusion of the 
generic attributes of the plane figure (Extension and Figure) along with 
;he special difference would make roundness, or the circle, a plural notion. 
Pleasure* is of the genus * feeling,' with a specific difference, which is 
i single property ; the genus and difference combined would give two 
properties. * Extended ' is absolutely single, being the highest genus of 
ill, on the object side. For the complete theory of Definition, this expla- 
aation is material ; in the present connexion, notions may be held as 
ringle. whenever the specific difference, usually assigned in defining them, 
is single. In many notions, this specific difference is complex. 
4 



C4 , NOTIONS, OR CONCEPTa 

♦• simple bodies of Chemistry — Oxygen, Sulphur, Silicon 

Sodium, •. — have each a series of distinctive pro- 

number actually known is considerable; and 

ij bo many unknown. There are from ten to twenty 

■ hi in the usual account of Oxygen ; and about as 

many in the description of Iron, and of Gold. 

ible world, we have classes founded on 
a great number of common properties. The classes termed 
in the peculiar sense of Species in the Natural His- 
bave a great many characters ;— many com- 
diarities in form, in mode of growth and development 
products, &c. A full account of the British Oak 
i to at least twenty or thirty characters 
in the Animal Kingdom, have we the aggregation 
rf m .resin the same class. The properties common 

Elephant' are very numerous ; a full enumera! 
be bodily and mental peculiarities of the species would 
re perhaps hhj to a hundred designations. TheTommon 
■ of the class W are still more numerous^ 
It is in these three great departments -the Mineral Ve^et- 

:: fr i ,h £ d ° .wSKste: 
:2„J, .sy^itr for •*?*' - 

u uy noc more than five or six distinctive 

; "» of each cLI S tlf 6 f kture ex P res sive 

it The san'e is t™ r V h ° S6 above ' and to ^ose 

same is true of the corresponding Abstrac- 

names '«eiuis' inri < «* • . 

,7. and species' express a single step 

Tl 1 

■ ^tr t heitr m r n rt s p de ^ ee ° f »»««%; a « 

of communion for ad m £ontTT 8 , haman bein S s ' the *e™» 
including h nm an\. ClaSS -, Th « class ' animal' 
■l«*-tl,e whoS of ? T! and a ^ reat ma °7 other 

~- *-,• co„ Pfi „ isjrsrzz-js'te 



GRADES IN CLASSIFICATION. 65 

widor class were termed a ' genus/ animals and plants would 
be species under it. The yet higher genus ' material bodies/ 
would have, as species, organized bodies and inorganic sub- 
stances ; and so on. 

Justice is included in the wider class ' virtue / virtue in the 
still wider, ■ human conduct.* ' Reason ' is a species in the 
genus • intellectual power ; ' which last is a species in the 
higher genus ' mental endowment.' 

Circle is a species in the genus ' curve line/ 

Geometry is a species in the genus Mathematics ; Mathe- 
matics is a species in the still higher genus ' science.' 

If we had no other terms of gradation but the two — genus 
and species — obtained from Greek philosophy, we should 
have to keep shifting them up and down the scale ; and they 
would express nothing but the relationship of the two classes 
indicated ; the genus would always be wider or more general 
than the species. But in Natural History, where there is a 
great range of successive gradations, a series of terms has 
been adopted to correspond to the entire compass of the scale, 
and each is retained for a distinct grade ; * genus* and ' species' 
being fixed at a certain stage, and kept always the same. Man, 
horse, dog, cat, are Species, and are never anything else ; the 
grades next above them are Genera and nothing else. 

In Botany, for example, there are four permanent leading 
grades, — Classes, Families or Natural Orders, Genera, and 
Species. The Dicotyledons are a Class ; Ranunculacece, is a 
Family or Natural Order ; Anemone a genus ; Anemone nemo- 
rosa (wood anemone), a species. In particular cases, inter- 
mediate grades are inserted. Classes are divided into 
sub-classes ; Natural Orders, are divided and sub-divided 
successively into Sub-orders, Tribes, Sub-tribes, Divisions, Sub- 
divisions ; genera into Sub-genera, Sections, Sub -sections; Species 
may have under them Varieties. The carrying out of these 
sub-divisions to the full would ranks fourteen grades. 

In Zoology, the primary divisions or sub-kingdoms, Verte- 
brata,Mollusca,&c.,are sub-divided into Classes (as Mammalia), 
Sub-Classes (Monodelphia), Orders (Primates), Sub-orders 
(Simiadae), Genera (Ape), Species (Chimpanzee). 

Beyond the Natural History departments, and one or two 
other exact sciences of classification, as Diseases, the terms 
'genus' and 'species' retain their mobile character. In 
Law, crime would be a ' genus ' to the particular kinds of crime 
— treason, murder, manslaughter, theft, libel, perjury, &c. 
4 Right ' is a genus to the several kinds of right ; it is a species 



H .sSES, NOTIONS, OR CONCEPT* 

rrnis ' claim/ or requisition. (G. C. Lewis, 
\ .lineal Terms,' p. 7). 

principle of Relativity, every class has its 
classes; every real notion has a co- 

s to be said on this head. The principle of 

true at all, must be true without reservation or 

We cannot form a class, without dividing the 

nto two halves, one half within and one half without ; 

te the class ' round ' in the universe 'plane 

mply certain other figures, as triangular, oval, 

which are the correlative group. The class 

another class, according to the universe of 

if that universe be actions relating to morality or 

evil, the negative or co-relative class is 'vice/ If 

be >\ < l(ii of. the class to be excluded or denied, may 

y be all material bodies. The class ' bitter 

m the universe 'sensations of taste/ co-relates with 

: stringent,' &c, or all tastes except bitter ; if the 

it ion,' the remaining sensations of taste, and 

nil i I us of all the remaining senses, are the correlative, 

s e\cluded when 'bitter tastes' are mentioned, the 

rward when bitter tastes are excluded. 

very abstract idea must have its correlative 

i] art, which must be a reality if the idea itself is a 

_th (in the universe ' dimension ') is opposed by 

Thickness. If 'justice' be a real notion, there 

lea reality corresponding to injustice. 'Affinity' is op- 

o 'neutrality ' or to 'repulsion,' or to both. If 

a distinct meaning in 'force,' there must be some 

:te; and the meaning changes as the intended 

it may be force as opposed to inactivity, 

e, or force as opposed to matter. 

UNLKB THE GTJISE OF THE PROPOSITION. 

y instances, propositions appear to give know- 
reality do not ; the intention being, not to 
ct things in affirmation, but merely to in- 
n, or Concept. This is a source of 
and fallacy. 

4 a triangle is a three-sided figure,' there is 






VERBAL PROPOSITIONS. 67 

the form but not the reality of predication ; in the sentence, 
' the pyramid is the form of greatest stability/ there is both the 
form and the reality. In the first case, what we conple, by 
the affirmation, is a name and a tiling; we give a lesson in 
naming, or else give the meaning of a name. In the second 
case, we couple two distinct things ; we declare a fact in the 
order of nature, namely, saying that wherever we find a build- 
ing of the form of a pyramid, there we have a structure of the 
highest stability. 

The instance first quoted — a triangle is a three-sided figure 
— typifies a large class of predications in form ; they are 
named ' verbal propositions/ 'definitions,' and also ' analytical* 
or 'explicative* propositions or judgments. Thus, 'Justice 
is the giving to every one their due,' is a verbal proposition, 
definition, or analytic judgment ; it tells us, that when the 
fact — 'giving any one their due' — occurs, the single word to 
name it by is 'justice/ and, conversely, when the word 
'justice' is mentioned, the fact signified is otherwise expressed 
or more fully unfolded by the words ' giving to all their 
due.' On the one side, such propositions teach us the name 
to apply to a given thing ; on the other side, they teach the 
meaning of a given name. 

In contrast to these propositions in form, the proposition, 
strictly so called, is a 'real proposition/ an affirmation (or 
denial) of conjunction, a 'synthetic 7 or ' ampliative ' proposi- 
tion or judgment, a declaration of the ; order of nature.' 

In verbal propositions that assert the concurrence of a name 
with a single feature of resemblance, there is seldom any 
mistake. Fallacies do occur in the more difficult and subtle 
questions ; as in Butler's allegations about Conscience and 
about Right. "When persons happen to be very ignorant of a 
subject, they may fall into the mistake of supposing the 
declaration of the meaning of a name to be the conjunction of 
two things, or two facts. Such ignorance is beyond the scope 
of Logic, which can only give warning of the ambiguous and 
deceptive character of the propositional form. 

'Homer wrote the Iliad/ is a verbal predication. We know 
nothing about Homer except the authorship of the Iliad. We 
have not a meaning to attach to the subject of the proposition, 
' Homer/ apart from the predicate, ' wrote the Iliad.' The 
affirmation is nothing more than that the author of the Iliad 
was called Homer. 

' Instinct is untaught ability' is a verbal proposition. If it 
imparts information beyond the use of the word instinct, the 



CLASSES, NOTIONS, OR CONCEPT* 

fafarmatian consists in substituting a precise statement of the 

, fur a vague and confused one All improve- 

delining of words have the same effect ; and may, 

han communicate a lesson in naming. 

pom the high function of a general name, which 

together widely distributed particulars. 

hereditary experience' (Darwin and Spencer), is 

,tion; the predicate is an entirely new fact, 

mprised under the subject, 

possesses authority over men's actions/ is a 
ition. When we enquire into the meaning, 
r definition of Conscience, we find that authority 
i-s; MMitial fact ; take away authority, and conscience would 
:it. There may be many real affirmations 
g Conscience. We may declare it to be — a simple 
A the mind, a compound or derived faculty, the vice- 
gerent of the Deity in the human mind, present in all men, 
absent in some men, absent in the animals, essential to human 
ty, the highest dignity of man. 
1 Matter is inert* is a verbal proposition ; it only repeats the 
essential quality of material bodies. Real propositions respect- 
matter would be such as these — Matter is, or is not, eter- 
nal; ractible ; is never at rest; is of many different 
Itates ; is endowed with numerous attractions 
repulsions, 
vernments are not made, but grow ' is real. 
t % Ja honourable,' ' virtue is lovely/ are real proposi- 
the supposition that we do not include approving 
nent in our ideas of those qualities. 
J Uninteresting sensations are never, for their own sakes, an 
ntion,' is a verbal proposition. The predicate 
p object of attention' means the same thing as the 
uninteresting sensations.' To interest us and to ex- 
■•ur attention have scarcely an assignable shade of differ- 
hongh it may happen that the use of the designation 
m th( e may assist a person little informed to see the 
full the designation in the subject. 

v is the authority of one or more men over 

en as the meaning of the word, and is there- 

n. All hypotheses as to the actual, or 

gm of the sovereign power, are real predict 

* When a class has several attributes in common, there 



CLASSES WITH PLURALITY OF ATTRIBUTES. 69 

may be the semblance of real predication, yet without the 
reality. 

1 A house is made to dwell in' is not a real proposition. ' To 
iwell in* is a part, although not the whole, of the meaning of 
i house. Whoever knows what a house is, knows the fact 
asserted in the proposition. 

* Mind is intelligent ' is a verbal proposition ; the predicate 
repeats what is already included in the subject. The connota- 
tion, or meaning of mind, embraces Intellect, together with 
two other functions — Feeling and Will. On the other hand, 
1 Mind is coupled with a material organization ' is real ; the 
predicate is no part of the meaning of the subject. We do 
not include the material accompaniment in the explanation of 
the word ' Mind/ Aristotle did include, in the meaning of 
' soul ' v^X'Vj the bodily organization ; to him, therefore, ' Soul 
is coupled with body' was a verbal or analytic proposi- 
tion. 

* Fire burns ' is not a real proposition ; it merely repeats, or 
unfolds, the chief attribute of the subject. Our earliest, and 
most persistent notion of fire, is the same as is expressed by 
* burning. ' 

9. In the Natural Kinds, verbal predication is still more 
apt to be confounded with real 

A natural kind is distingished by containing not one, two, 
three, or four features of community, but a very large, indefi- 
nite, and perhaps inexhaustible number — twenty, fifty, or a 
hundred. Oxygen has a great many properties ; the aggre- 
gate of all these is properly the meaning of the word. Oxy- 
gen is a gas, has a given atomic weight, combines with hydro- 
gen, &c, — are all in strictness, verbal or analytic propositions. 
Are they therefore useless or incompetent ? Certainly not, 
yet their form is somewhat misleading. 

The technically correct form of these predications would be 
as follows : — There exists in nature an aggregate of the follow- 
ing properties : — matter, transparency, the gaseous form, a 
certain specific gravity, active combining power, and so on ; — 
to which aggregation is applied the name ' oxygen.' After 
the information thus given is fully imbibed by the hearer, the 
propositions * oxygen is a gas,' ' is an active combining agent,' 
&c, are verbal, identical, or tautological propositions ; the pre- 
dicates, being suggested to the mind when the name is pro- 
nounced, are a superfluity. 



{2d*e 



70 CLASSES, NOTIONS, OR CONCEPTa 

;rp, however, certain circumstances and occasions 

predications are not identical or tautological, but 

te adding something to the subject as under- 

n may be insufficiently informed as to the pro- 
lin complex class, but yet may know enough 
i the class. Most people know that an elephant 
imal, with thick skin, a trunk, and ivory tusks, 
ucli a state of knowledge, the affirmation of any one of 
ts would be a verbal or identical proposition; it 
y repeat one of the facts already entering into 
ping of the word. But the elephant has a great many 
iliaritics besides ; and the communication of any of these 
Id be real knowledge; they would be 'synthetic' affirma- 
nts added to what is already implied by the 
■ Iter being communicated, understood, and im- 
ii the memory, they would cease to be real predica- 
; they would henceforth be verbal or analytic state- 
is ; repeating what the name now suggests or connotes to 
! <rson whose information has been enlarged. 
; newly discovered properties are real predications on 
Bret announcement; although immediately on being 
mumcated, they become verbal. When Faraday discovered 
gen is magnetic, the intimation of the fact was for 
tl.e moment a real proposition respecting 'oxygen'. After 
ce communicated, it was no more real than the 
l nation of any other property of oxygen. 

the £?£!?%? ^ inducUve <>P eraii °» squired to ascer- 
u.i'vVof V 6 P ro P erties of a complex class or notion 

SXt "wm Dr a e nd ST 9 ' ^ t ^ * 
neinductmn to V. nd Jh°ugbt ;-but this sup- 

•cur f !f i ' I? 0W that these thre e properties 

eTre is S re tn here - iS **■»& there » -l-o Will, 

,,„, Wll and ih nn JL 1S alS ° Th ° U S bt ' To afSm 

Tne a limtL f fr * , are associ ated, is a real pro- 

ion ia elb 1 / \ Imd tadt] 7 a ssumes that this 

Ss are lerbat 'n ' ^ Mi ° d feels > Mi * d ™ 1,s - 

r ihaffi tb °^- * Tet ' SinCe ««* im ^' 

be c on, f dlStmCt fa0ts * re ™ ited iD 

mHeath. rCd ** havin S the reality of 

"u C o r ns t ^;f n r r r t r!~' ,Cheinical affini *y * * 

- a *££T£ft " follo r d . h y <*&>& ° f 

ert)al or analytic affirmations 



THE DEFINITION. 71 

-et, there is a reality at bottom; namely, that 'union in 
[eft trite proportions is conjoined with evolution of heat and 
hauge of properties.' The name ' chemical affinity p covers all 
bree facts ; and when used as a subject, with any of them as 
redicatcs, the affirmation is strictly verbal or identical ; the 
rord already means what is affirmed.* 

The cases now quoted differ essentially from the aggregates 
lied ' kinds ' — mineral, vegetable, and animal bodies, for 
easons to be afterwards given. 

(3) The verbal proposition may be not improperly used as 
reminder, or by way of referring to, or reciting a known fact. 
Ve may say ' oxygen is the supporter of combustion/ intend- 
ng only to bring to mind or to indicate that special property 
rith a view of making some inference from it. Jt is as if we 
rere to say — ' inasmuch as among the aggregate of powers and 
>roperties named oxygen, one is the support of combustion, 
herefore, &c/ 

10. The verbal proposition is, to a great extent, identical 
nth the Definition, which has the form of predication, 
>ut is in substance coincident with the Class, Kotion, or 
Concept. 

In defining, we use the form of the proposition ; — 'a square 
3 a straight-lined, four-sided figure, with its sides equal, and 
ts angles right angles;' *a society is an aggregate 
f human beings under a common government.' But the 
lliance indicated by the affirmation i3 not between two things, 
mt between a name and a thing, so that all definitions are 
rerbal propositions ; and all verbal propositions, relating to 
general words, serve the ends of the definition. The examples 
hove given of the verbal proposition admit of being expressed 
s definitions, in whole or in part. * Matter is inert' may be 
, r iven as the definition of matter. * Oxygen is a gas,' is part 
>f the definition of oxygen. 

11. The Definition, in its full import, is the sum of all 
he properties connoted by the name. It exhausts the 
neaning of a word. 

* Many words, from the circumstance of naming complex notions, 
oveitly affirm propositions; they cause it to he supposed that the con- 
unction cf the several properties has "been already verified ; which may 
r may not have been the case. The name ■ substance ' means a self- 
ubsisting entity, underlying and supporting the attributes of things , it 
•ting taken for granted that there is in nature such a conjunction, 
jciitham described certain names as * question-begging appellatives,' 
>ecause they could not be used without assuming the truth of propositions. 



CLASSES, NOTIONS, OK CONCEPTS. 

.nit ion of * Wealth ' is a statement of everything in. 

wing of the word. The definition of * Mind 

s requisite to whatever we call a mind. 

12. Winn a thing has numerous properties, as in the 
ural Kind, certain purposes may be served by 
definition. 
(1 [of our enumerating all the properties essentia] 

I, we may mention only those that are sufficient foi 

ing it from other kinds. Thus gold could be defined 

as yellow, incorrosible, and having the specific gravity 19*34; 

no other substance possessing the same combina- 

qualities. Mercury is the metal that is liquid at 

oommon temperatures. The banyan tree sends down numerous 

which take root and prop up its branches. The ele- 

u Id ho defined by his trunk alone ; this would be 

»ugh to prevent his being confounded with any other 

annual. 31 an could he defined by the number of his muscles, 

ire of his hand, or his mental faculties, all which are 

iliar to humanity. 

These are the definitions that serve for discrimination, 

or diagnosis. Weight and colour together are suffi- 

■t a bad sovereign. In chemical testing, two or 

properties are sufficient to identify a substance. There 

es known by a single symptom ; the deposition of 

happens only in gout. 

if sufficiency of such definitions is owing to the absence 

Uier things possessing the same features. New discoveries 

may take away this advantage. The high specific gravity and 

lour of platinum failed as decisive tests when the allied 

metals, osmium and iridium, were brought to light. If there 

idrupeds possessing the mental faculties of man, these 

won Id no longer suffice to identify a human being. 

icn definitions, although unexhaustive or incomplete, 

1; fl f ls of the thing defined; they are included 

;<; marks or characters believed to be inherent in the 

Ihere maybe other characters, serving the purpose 

S'";tf' ?** ar f. *«**«* ^ not essentials/ Thus, 

; aeculent of the diamond to be, quantity for quantity 

precious substance in nature. It is the accident of 

o be the paragon of animals; ' what we regard as the 

•« -- of h umanity would Btm Eemai * alth0 h a 

re to appear on the earth. ^ so long a* 
■m distinctive, they serve for a definition" in 



GENUS, SPECIES, AND DIFFERENCE. 73 

the sense of a test ; they prevent the thing from being con- 
founded with any other thing known at the time. 

If we know a thing only by such discriminative tests, the 
other properties, when predicated of it, make, not verbal but, 
real affirmations. Yet, as soon as we learn these additional 
properties, we must regard them as falling under the connota- 
tion of the word. When we are told that diamond, which we 
knew to be a transparent, glittering, hard, and high-priced 
substance, is composed of carbon and is combustible, we must 
put these additional properties on the same level as the rest ; 
io us they are henceforth connoted by the name. 

THE FIVE PREDICABLES. 

13. The Five Predicables relate to the distinction be- 
tween verbal and real predication. They are Genus, 
(7^09), Species, (elSo?), Difference, (Sta^ooa), Property (JSiov) 
Accident or Concomitant (o-vfiftefirjKos). 

The three last— Difference, Property, and Concomitant — 
are the predicates strictly so called, as illustrating the distinc- 
tion above mentioned. The two first — genus and species — 
have nothing to do with predication in the sense of the others. 

Genus, Species, and Difference are mutually correlated ; 
each involves the two others. We have already given the 
meanings of Genus and Species ; we have now to add th© 
meaning of difference, which is involved in these. The Dif- 
ference expresses the characters possessed by any species, over 
and above the characters of the genus. If we suppose * wolf to 
be of the genus canw, the characters belonging to the wolf, in 
addition to those of the genus, are the Difference, Differentia, 
or specific difference of the wolf. In short, the surplus of con- 
notation of the species, as compared with the genus, is tho 
Difference. 

4 Science ' being called a genus and * chemistry ' a species 
under it, the differentia of chemistry is what distinguishes it 
from other sciences, what it has peculiar to itself, besides the 
generic features of a science. 

Of the three facts — genus, species, difference — given two we 
infer the third. From the genus and the species, we can tell 
the difference ; we have only to subtract the essential attri- 
butes of the genus from the essential attributes of the species. 
Given the species and the difference, we can find the genus by 
subtracting the difference from the attributes of the species. 



74 CLASSES, NOTIONS, OR CONCEPTa 

n the penns and the difference we can fix the species, by 
■dii. ic marks to the difference. Fine Art bein<* t. 

'>, and J '. B] tcics, the difference is the medium or 

...ty of colour. 

11 A short, and yet complete, form of Definition is to 

me lusher genus of the thing defined, together 

ilic difference. In popular language, de'fininw 

.'us form, and it has been improperly re- 

iogiciaus as the regular and only form. 

logy is de6ned the Science (genns) that treats of 
/ bodies (difference). Poetry is a Fine Art 
having hinguagefor its instrument (difference) 

eech being addressed to persons already partially 

I, it is usually sufficient to define in this way. The ner. 

definition of Physiology is supposed to.be already 

with the generic idea of science. If this is not the 

■ be : e ho.t.on fails. Science itself would require defini! 

eference to a higher geuus as 'knowledge,' and soon. 

attrfbuts , n , ; e tl attributes «f the g^us, and the additional 

"d r, tJ e «Pecie8 (that is, the difference) are con- 

5EKTIAL attributes. They are all included 

ffimaSTofV CUn r tati ° U ° f the — Hen e" e 
-turn ot these makes a verbal (or essential) predica- I 

I Co^ant mDS b6adS ° f P^dic t ation ) -Pro- 

'. "aiSute S? 1 ^' be, ° ngS t0 real Predication 

■■»■ S^wSSS^ deduced from ' or de - 

'It • * 

»• *SS'frTi!S 'Ttffu' 0r defi ^'«on of a triangle 

,k ' ti " i '-n /SIT fr? SideS - There foi^ 

latingt fhe?r1 ' C f deduction > a great many 

»•' These fall aider thl head ai !ff S V «V* to tw0 ri * ht 
e bead of Predication called 'pro- 



PK0PR1UM. 75 

perty ' or proprium ; they are not essential characters, although 
derived from essential characters. They typify one large 
department of real predication — the propositions obtained by 
mathematical inference. 

Again, * oxygen supports combustion ' is not an essential 
quality of oxygen ; it is a proprium. It is clearly deductible 
from the more general quality of oxygen expressed by its com- 
bining powers : it is more immediately derived from the fact 
that oxygen combines with carbon. 

From the specific gravities of a number of substances (an 
essential quality), we can deduce a great many propria. Com- 
paring, on the point of specific gravity, mercury with platinum 
and gold, we infer that platinum and gold will sink in mercury ; 
ei similar comparison would show that iron, tin, copper, lead, 
silver, &c, will float. These are deduced propositions or pro- 
pria, and not essences ; they are not generic, specific, or 
differential characters. 

4 Fluids press equally in all directions' is a proprium; it 
follows from the definition of fluidity. 

The power of speech is not an essential or defining character 
of man ; it proceeds from his other endowments of body and 
Df mind ; it is a proprium. 

We see, therefore, that to keep up the distinction of essence 
ind property, it is requisite that the essential or defining marks 
:>f a thing should be ultimate and distinct, and not resolvable 
into one another. If a quality could be shown to flow from 
?ome other quality, it would cease to be an essential or defining 
nark, it would be an inference or proprium. The distinction 
s lost, when we mix up indiscriminately ultimate characters 
svith derived characters, as is not unfrequently done in the 
sciences, as well as in popular usage. The enumeration of 
:he attributes of oxygen, of gold, of man, should be an enume- 
ration of the final (so far as can be made out), the underivable 
Dowers or functions of each. 

The proposition ' Man is rational' is a proprium. The ultimate 
tnalysis of man's mental nature, to which * rationality ' is 
•eferable, shows that reason is not a fundamental operation, 
)ut derived from the foundations of the intelligence ; whence 
his should not be given as part of a scientific definition of 
nan. 

The same may be said of * Man walks upright ' ; which is 
in easy inference from his anatomical structure. So also * man 
8 a cooking animal, ' would be an application of a more 
general fact — man is a tool-using animal ; which is itself a 



76 CLASSES, NOTIONS, OR CONCEPTS, 

m his muscular endowment combined with hia 

•ion - man is mortal' is expressly given by Mr 

ify real, as opposed to verbal, predication. If 

m . To decide the question, however, we 

i bare to go back to the mode of stating the peculiar 

:e d beings that refers to their germination 

, . Should the cycle of existence signified 

words be reckoned an ultimate, or unanalyzable attri- 

g beings, mortality would be of the essence of 

ol all animals, and all plants; and therefore to affirm 

verbal or essential predication. 

1 7. The Accident or Concomitant, in Predication, ex- 

thing neither belonging to the essence or con- 

of the subject, nor deducible from it. ' Gold is 

valuable of the metals/ 'is used for the coin of 

.aha— are propositions where, the predicate would be 

called an Accident or Concomitant. 

The real proposition, as opposed to the verbal, essential, or 
teal (Kant's analytic judgment), reaches its highest point, 
in this species of predication. It gives us the full meaning of 
's * synthetic judgment/ where the predicate is a positive 
addition to the subject, and neither directly nor indirectly ctfn- 
miler it. 
These allirmations of concomitance are exceedingly abund- 
ant in everyday practice. "We are constantly finding about us 
things joined together, without mutual implication. All the 
affirmations respecting material bodies that deal with their 
distribution, their quantity, their uses, — are affirmations of 
miitance ; we do not include these points in the defini- 
tion or essence. It is the essence of gold to be incorrosible 
(unless it were to be found to be derivative, or a proprium) ; it 
I the essence to be used for coin, or for ornament; still 
occurring in California and in Australia. We should 
hink of including these facts in the definition of gold. 
ipeetfio gravity is an essential quality (to all appearance^) ; 
and doubtless the position in the older and deeper rocks is a 
consequence of this, and might be called a proprium of gold. 
1 lie putting forth of energies into actual display is the occa- 
of propositions of concomitance Socrates sits, walks, 
e real predications. All the shifting usages, habits, 
and positions of things, are in like manner real :— he is in good 






ACCIDENT OR CONCOMITANT. 77 

health ; the mountain is covered with snow ; the crops are 
ripe. 

Among the highest propositions of science, as will be seen 
afterwards, there are few predications of concomitauce. 

18. A distinction is made between separable and insepar- 
able Concomitants. The inseparable Concomitant is scarcely 
distinguishable from the Essence. 

The separable concomitant is what we commonly mean by 
Accident ; as ' gold is found in California.' We see plainly 
that this depends upon arrangements where other matters 
besides gold are concerned ; and which might have been 
different without any alteration in the qualities of gold itself. 
That geese were kept in the capitol of Rome, was an accident, 
a separable concomitant, of the goose. 

The standing example of this distinction in the old logical 
books was 'Virgil resides in Rome' (separable), 'Virgil was 
born in Mantua ' (inseparable) ; a distinction sufficiently real, 
bat practically worthless. 

The inseparable concomitant is exemplified in the colour of 
those animals whose colour has never varied ; as was so sup- 
posed to be the case with the whiteness of the swan and the 
blackness of the crow. If we were to ask why an attribute 
always present in a species, and not known to be a proprium, 
was not adopted into the Essence, we shouid probably be told 
in reply, that the colour of animals is an unstable property ; 
it often varies when everything else seems to remain the same ; 
hence it is usually left open in assigning the marks of species. 
The cases quoted justify the practice. Neither the whiteness 
of the swan, nor the blackness of the crow is universal in those 
species. 

These remarks on the Predicables will serve to bring out 
into farther prominence, the distinction between Verbal and 
Beal predication. 3 



CHAPTER IH 
PKOPOSITIONS. 

1. -The Proposition lias been already viewed as made up 
of Subject, rivilit'iite, and Copula. 

In common with names, and with notions, Propositions 

ified (I.) according to Generality, and (II.) ac- 

ling to Relativity. 

We now enter upon the full consideration of the Real Pro- 
position, where there is both the appearance and the reality of 
on. 
It is of importance to view propositions, as we have viewed 
d concepts, with reference to the two fundamental 
mtea of knowledge — Agreement and Difference, or Gener- 
ality and Relativity. 

Propositions follow concepts in being of different grades i 

a Li it. ' The St Lawrence falls at Niagara ; ' * all water 

nus;' all terrestrial bodies gravitate towards the earth's 

k the bodies of the solar system gravitate towards each 

• '; ' all matter gravitates ;'— are propositions of successive 

ees of generality ; each takes a wider sweep than the pre- 

. till we reach the widest of all. ' People should be taught 

take cold'— 'to take care of health' 'to be prudent !,' 'to be 

**,— are four propositions rising in generality. 

It is obvious that the generality of the Proposition follows 

f the concept or notion. Any proposition re- 

mg the Earth, is merged in a proposition respecting the 

a proposition respecting the Planets is less general 

respecting Heavenly Bodies. The more general the 

pt forming the subject of a proposition, the more general 

Bition : 'men, animals, organized beings,-are liable 

•of inverse relationship of Extension and Compre- 
Deno tation and Connotation, applying to the notion, 
o to the proposition. The most highly generalized 
ns are those that have the smallest predication ; the 
gradually lessened as predication is increased, We 



GENERALITY OF PROPOSITIONS. 79 

mj 'all matter is indestructible ;' but when to the property of 
indestructibility we add the property — unchangeable in state 
(as regards solid, liquid, gas) — we have to limit the subject to 
a tew bodies, as to the (hitherto) uitcundeustble tjasen and to 
carbon* 

II. Propositions come under Relativity, in this respect, 
namely, that to every proposition there exists a correlative 
proposition, something denied when it is affirmed. ' Europe 
lies north of the Equator ' — ' Europe does not lie south of tho 
Equator ;' ' friendship is pleasure ' — * friendship is not painful 
nor indifferent.' 

Here, too, the proposition follows the notion. To every 
intelligible notion, there is an intelligible opposite — something 
that remains when the notion is subtracted from the universe ; 
south is opposed by north (universe 'north and south') ; plea- 

* ' The circumscription of general maxims, with reference to actual cases 
of practice, is thus effected by adding the circumstances of the given case, 
aud considering the combined result. A general theorem is founded on a 
limited set of hypothetical data, and the more limited they are the more 
abstract is the theorem. The intensity varies inversely with the extent of its 
signification. Now a theoretical proposition, when converted into a rule of 
conduct, may be conceived as taken in connexion with an indefinite number 
of sets of concomitant circumstances, which may modify its operation. If, 
therefore, we add a definite number of circumstances to the proposition, we 
exclude all uncertainty as to the possible combinations, and we in fact 
perform a sort of practical abscissio infiniti. We substitute a real and 
definite for an ideal and indefinite compound. The addition of a limited 
number of terms operates as the exclusion of an unlimited number. 

* Thus, let it be supposed that our general theorem is as to the operation 
of legal punishment. Legal punishment, if left to itself, may be expected 
to produce abstinence from crime ; but it may be accompanied, and as it 
were, held in solution by a vast variety of collateral circumstances which 
may influence its operation. Thus, it may be combined with an inefficient 
or unskilful police, a venal, or tardy administration of justice, difficulty of 
detection, unwillingness to prosecute or to give evidence, or a fanatical 
contempt of suffering. Various other circumstances might likewise be 
mentioned which diminish the deterring force of the fear ot legal punish- 
ments on the minds of given individuals. Now, all that can be said with 
reference to such a general theorem, so long as it remains an abstraction, 
is that it describes a prevailing tendency, liable to be resisted and modi- 
fied by an unlimited number of counter-influences with which legal 

' punishment may be combined. But when an actual case is laid before us, 
we can perceive whether any is, and which of those other circumstances 
are present. Of such as are wanting we take no account, we note those 
which are discernible, and we then form a definite practical problem, in 
this shape": * How will the denunciation of legal punishment operate, 
taken in connexion with a reluctance of witnesses to give evidence or with 
a willingness of judges to take bribes (as the case may be) P ' What will 
be the effect of legal punishment, combined with a hope of impunity, or a 
disregard of pain, of some special ascertained nature P" (G. C. Lewis\ 



8Q PKOPOSITION& 

imro il opposed by the two states— pain and indifference 

( m,i linLr')- . i. ii i-i x xi 

beta two fundamental distinctions, applicable alike to the 

i the Proposition, being presupposed, we proceec 

of Ileal Propositions that have a bearing 

. , i .. The primary division is according to Externai 

, and according to Import, or Meaning, in the fina 

ana! . 

term ' Judgment' is used in most logical treatises to desig- 

the proposition. A proposition is stated to be * a judgment 

in words ;' and Judgment is termed the mental operation 

we pronounce two things to agree or disagree. When we 

i a mountain to be four thousand feet high, we pronounce the 

the height of the mountain with the lineal quantity 

>ur thousand feet ; we of course imply the disagree- 

with any other quantity more or less. 

It may be remarked on this employment of the word Judgment, 

in connexion with the proposition, that, in the view of Aristotle, if 

i real significance. Aristotle took account of the subjective 

nt of affirmation, the implication of the individual mind of 

.Hrnier in the process. When I say, * the earth is round,' the 

full import is that, according to my belief, conviction, or judgment, 

nth is round ; or I believe that the earth is round. I speak 

only for myself. I cannot undertake to say what other people 

v \ unless they tell me; and, apart from all belief, the propo- 

D has no meaning, no existence. 

For almost all practical purposes, this indispensable correlate 

be left in a tacit condition. Being always presumed, it need 

e mentioned. In many other cases, we suppress the mention of 

what we can always count upon, as for example, gravity. We do 

not say that a certain weight will maintain the movement of a 

provided gravity continue to operate ; we take this for granted 

w i t hout specifying it. But there are occasions when the correlated 

subject in affirmation needs to be brought into view; as when 

hy.sicians declare that there can be objective truth without a 

t; and when certain opinions are sought to be imposed by 

. as absolute and infallible. 

^rtfrom this circumstance, the term Judgment is not the 

apposite word for expressing the formation of propositions. 

unction of a judge may require propositions to be stated; but 

illy it consists in discerning the agreement or disagree- 

proposition with a given case ; as in the interpretation of 

J he faculties needed for arriving at propositions are much 

than is meant by judgment ; the processes of obser- 

issification, induction and deduction, bring into play 

1 the intellectual powers in their widest Icope. 

It is incorrect and misleading to describe a proposition as 

judging two notions to be congruent; 'conceiving them as one' 



QUANTITY OF PROPOSITIONS. 81 

(Hamilton). All that a proposition can do is to link together two 
facts (as ' fluid ' and * level '), it does not in any sense make them 
one fact, or bring the one under the other. 

EXTERNAL FORM OF PROPOSITIONS. 

2. Propositions aie either Total or Partial, which dis- 
tinction is expressed by the word Quantity. 

Universal and Particular are the names most used, 
although not the aptest, for signifying this division. 

When the predicate is true of the subject, in its whole 
extent, or in every instance, the proposition is total or universal 
in quantity ; — *all the planets are round '; * all the virtues are 
useful '; ' all coal is the product of ancient vegetation'. 

When the predicate is true of the subject, only in part of its 
extent, or in an indefinite number of instances, it is partial or 
particular in quantity : — ' Some planets are larger than the 
earth;' 'some of the virtues are painful in the performance;' 
' some coal is useful for making coal gas ' ; ' some men are 
wise' ; * some metals are incorrosible' ; ' some crystals are 
transparent' ; ' some diseases are incurable.' 

The usual designations for total or universal quantity are 
'All' and * Every.' 'All earths are oxides of the metals'; 
' every man is expected to do his duty/ There is a rhetorical, 
but no logical distinction, between the two ; • every ' has the 
emphasis of greater individuality. ' All ' is sometimes ambigu- 
ous ; it may be used in a collective, as well as in a distributive 
sense; 'ail England' may mean the whole nation in a col- 
lective capacity, and not ' every Englishman.' 

Universal quantity is sometimes given in less explicit forms : 
— ■ The earths are oxides/ ' evil-doers need to be punished/ 
* man is frail/ 'pleasure tempts,' 'alcohol is a stimulant,' — are 
understood to be universal, although they have neither the de- 
cisiveness nor the emphasis of the other forms. 

The term of Partial or Particular quantity is ' some/ — mean- 
ing an indefinite number, one or more, and possibly all. It 
negatives ' none,' without saying how many. The logical 
'some' is expressed by the phrase ' some at least.' The ' some ' 
3f common speech is different ; ' some men are wise/ ' some 
fever patients recover/ are interpreted as implying that there 
are some men that are not wise, and some fever patients that 
will not recover. When we assert a quality of a subject that 
we are acquainted with, we are usually aware that while some 
instances possess the quality, others do not ; the use of 4 some ' 



I 

82 EXTERNAL F01M OF PROPOSITIONS. 

does not express our ignorance of the others but rather oni 
hat these are deficient in the quality, This is fullj 
seme at most/ a small or limited number, in com- 
ison with the whole. The logician's view of ' some woulc 
,nd to a case of first contact or encounter with a ne* 
Thus, a voyager in landing on a newly dis- 
inrl meeting a lew of the inhabitants, while as 
►rant of the general mass, would say 'some are lank- I 
I ;' he would speak of those he saw, and of no more. 
" The logician's 4 some' is rarely found in common use. The 
rd itself is frequent enough ; but in using it, we are aware 
that there is an actual limitation of the subject. The logical 
importance of the word comes out in the conversion of proposi- 
tions, with a view to the syllogism. As, in nearly every I 
affirmative proposition, the predicate is larger than the subject, j 
includes the subject and something more, we can never trans- 
pose the terms (in conversion) without a qualification; 'all 
men are mortal,' if transposed, must be ' some mortals are 
men/ 

In what is called the 'minor term ' of the s}dlogism, ' some' 
can be replaced by any other word of quantity, as one, ten, 
few, a small number, many, &c. ; the same word being trans- ] 
fcrred to the conclusion keeps the syllogism correct. But in 
the really important case — the expression of a universal affir- 
mative, in transposed terms, we are restricted to ' some ' or 
• part.' 

The reason why ' Universal ' and * Particular' are not suitable 
names, for the two modes of quantity, is that these names desig- 
nate also the inductive contrast between a general proposition and 
the particulars or individuals that we derive it from. The distinc- 
tion of General and Individual belongs to the substance and not to 
the form of propositions ; it is their inductive and not their deduc- 
tive, or formal aspect. 

Mr. De Morgan (Syllabus, p. 60) proposes the terms ' full ' and 
4 vague' as other synonymes for the objectionable couple — Universal 
1 Particular. • All Men ' is full extent ; ' some men ' is vague 
extent. 

Another term for quantity less than total, is 'Most ; ' which 
has been introduced into the syllogism by Mr. De Morgan; 
'most gases are odorous :' 'most of the cerebral nerves spring 
from the medulla oblongata;' ' most plants are hermaphrodites.' 
Certain forms of the proposition have been called Indefinite 
in quantity ; the expression leaving it uncertain whether they 
are universal or particular. They are, in point of fact, am- 
uuiis. The chief examples occur with names of material, 



QUALITY OF PROPOSITIONS. 83 

tich are the subjects, sometimes of universal, and at other 
times of particular, predication. 'Food is chemically consti- 
tuted by carbon, oxygen, &c.' is a proposition of universal 
quantity; the meaning is all food, all kinds of food. ' Food 
is necessary to animal life' is a case of particular quantity ; 
the meaning is some sort of food, not necessarily all sorts. 
: Metal is requisite in order to strength ' does not mean all 
kinds of metal collectively. 'Gold will make a way' means a 
portion of gold. 

The term * Distribution * or ' Distributed ' is a technical, 
but not veiy suggestive, term for universal quantity. With 
the universal designations ' all/ ' every/ or their equivalents, 
a subject or predicate is said to be distributed ; a particular 
form ' some ' is said to be undistributed. 

3. Propositions are either Affirmative or Negative ; a dis- 
tinction according to Quality. 

A proposition either affirms or denies a predicate of a sub- 
ject; 'Wine is good/ 'wine is not good.' Two properties 
either co-exist or do not co-exist ; and to be informed of non-co- 
existence is as important as to be informed of existence. ' The 
moon is up/ ' the moon is not up/ are propositions equally valu- 
able as knowledge ; we are guided by the one no less than by the 
other. 'He is guilty,' 'he is not guilty/ are fundamentally 
different assertions ; each drawing its own consequences with it. 

Affirmative and Negative propositions are not merely differ- 
ent, they are ojjposed ; which signifies that by interpreting the 
opposition, we can make out all the consequences of the one 
from the consequences of the other. With the same subject 
and the same predicate, affirmation and denial are so implicated 
together, that if we know what the affirmation means, we also 
know what the denial means. One effort of understanding 
serves for both. If we are told that ' the accused is guilty/ 
involves a fine of five pounds ; we know also that the negative, 
'the accused is not guilty' involves exemption from the fine. 
This is merely an aspect of the Law of Relativity ; according 
to which the knowledge of opposites is one. 

Some logicians have proposed to do away with the distinction 
between affirmative and negative by transferring the sign of 
negation from the copula to the predicate ; ' A is not B/ ' A is 
aot-B ; ' 'penury is not agreeable/ 'penury is disagreeable.* 
There is then the appearance, but only the appearance, of making 
ill propositions affirmative. The attempt is illusory. Affirmation 
and Denial belong to the very nature of things ; and the distinc- 
tion, instead of being concealed or disguised to make an imaginary 

(A ~ ., V* 



0- 



vy> 



84 EXTERNAL FORM OF PROPOSITIONS. 

unity, sli.ml.1 receive the utmost prominence that the forms oi 
Unguagq can bestow. 

sides being either universal or partial in quantity, 
position is either affirmative or negative. And, by the 
I ilatmty, to every affirmative form there corresponds 
:itive form, both understood if one is. 
Ration is complicated by the quantity of the propositions 
opposed. The simplest form is 6een in the opposition of a uni- 
versal to a universal — 'all diamonds are precious/ i no dia- 
monds are precious,* or when the subject is a definite indi- 
vidual, as 'Francis was (or was not) the author of Junius.' 
When a particular is opposed either to a universal, or to 
another particular, there arise distinct forms of negation or 
contrariety, which will be described presently. 

4. The negative words ' not/ c no/ and their equivalent 
prefixes and suffixes, are the explicit forms of negation. 
There are other forms of a less direct kind, 

For the negative of a definite particular proposition, as 
4 John is here/ * the day is fine/ we prefix not to the predicate, 
4 John is not here/ For universal propositions, this mode is 
insufficient ; 4 all planets are round/ is not negatived by * all 
the planets are not round / the meaning of such an expression, 
according to the idiom of our language, is, that some planets 
may be (and probably are) round, but a reservation is made of 
the rest. We arrive at a thorough negation, to the complete 
denial of the universal affirmation, by prefixing the negative 
adjective 'no* to the subject — 4 no planets are round/ 

4 No useless coffin enclosed his breast ;* 

Another form, adopted for rhetorical emphasis, is seen in * not 
a man escaped/ 

' Not a drum was heard, not a funeral note.' 
The prefixes 4 in/ ' un', and the suffix 4 less/ are equally 
emphatic. 4 All his actions were just (unjust), wise (unwise), 
prudent (imprudent)/ 4 The country in stony Arabia is water- 
less and treeless.' 

Negation may be conveyed by such phrases as ' far from, 

4 the reverse of/ 4 on the contrary/ 'wanting or deficient in/ 

devoid of/ <fcc. Certain words, as 4 few/ 'hardly/ 'scarce/ 

hare a positive or negative effect according to the context. 

admits a small number, and denies all beyond ; occa- 

dly it is a polite form of total denial. In some cases, the 

meaning is positive, the stress being laid upon the small 



SIMPLE AND COMPLEX PROPOSITIONS. 85 

amount of admission ; in other cases, the force is meant to be 
negative, 'few will see that day.' 

5. Propositions are either simple or complex, a distinc- 
tion only partially belonging to Logic. 

In a simple proposition, there is bat one subject and one 
predicate: 4 the sun is up/ 'justice is excellent,' ' Britain has 
numerous colonies/ In a complex proposition there are more 
than one predicate or more than one subject, or both. 
'Britain, France, and Prussia are maritime powers / ■ Britain 
has often been at war, and has acquired foreign possessions.' 
In the first example, three propositions are combined in one 
common predicate ; and should they require to be logically 
canvassed, they must be taken separately : 4 Britain is a 
maritime power/ &c. In the second example, two propositions 
are affirmed, and one implied, although there is but one subject 
'Britain.' It is affirmed (1) that Britain has often been at 
war, (2) that Britain has acquired possessions abroad ; and 
the close connexion of the two statements, is meant to convey 
an additional circumstance, namely, that the second fact was 
the consequence of the first. As before, these allegations would 
be taken in their separate and simple form, in any question 
as to their truth or falsehood, or as to the evidence in their 
favour. 

The whole of this class might be called Compound, instead 
3f complex, Propositions. 

6. The Complex Propositions more especially entering 
into Logic are of two kinds, named Conditional and Dis- 
junctive. In these, the separate propositions are conjoined 
in one meaning. 

The Conditional Proposition is extremely common; it is a 
statement with a qualification ; ' if ignorance is bliss, 4 tis 
folly to be wise' ; ' if every one speaks together, the business 
cannot be done ; ' ' unless rain come, the crops will fail-' 

This form is also expressed by saying that one statement is 
:he consequence of another; or that there is an affirmation of 
:he consequence or connexion of two facts ; that where one 
act is present the other fact will follow, these facts being ex- 
Dressed in propositions. Thus, ' the consequence of ignorance 
jeing bliss is, that it is folly to be wise ; ' ' the consequence of 
)very one speaking together, is that no business is done / ' the 
Jonsequence of a want of rain will be a deficiency of the crops/ 



86 TEKNAL FORM OF PROPOSITION& 

ill such cases, it is only a matter of course, that supposing 
the antecedent present, the consequent is also present. 

Disjunctive Proposition expresses an alternative : « John 
U either in the house or in the office' ; 'granite is either a 
mentary deposit or a product of igneous action ;' 4 to be or 
not to be, that is the question.' 

se propositions may be viewed as condensing alternative 
conditions; 'If John is not in the house, he is in the office ; 
and if be is not in the office, he is in the house.' 

Each class is the basis of a distinct species of logical trans- 
formations, constituting a supposed variety of the Syllogism. 
The name ' hypothetical' expresses both the conditional and the 
disjunctive forms, and is opposed by * categorical' which desig- 
nates all other propositions. 

7 The combination of difference in Quantity with 
difference in Quality, gives rise to four classes of Proposi- 
tions : — 

(1) Universal Affirmative (A) 

(2) Particular Affirmative (I) 

(3) Uuiversal Negative (E) 

(4) Particular Negative (0). 

These propositions are expressed symbolically by the letters 
A, I, E, 0. The first and second forms, the affirmative, derive 
their symbols from the vowels of the word Affirm : A being 
the universal, I, the particular affirmitive. The third and 
fourth forms, the negative, derive their symbols from the vowels 
of nEgO; E being the universal, and O the particular negative. 

A — All men are fallible : all X is Y. 

I — Some men are wise : some X is T. 

E — No men are gods : no X is Y 

O — Some men are not wise : some X is not T, 

Hamilton's Quantification of the Predicate. 

8 These are all the forms admitted into the usual 
syllogism, being sufficient for ordinary pnrposes. We 
may notice, however, in all of them, that the quantity 

ken of has reference to the subject ; and nothing is said 
explicitly of the quantity of the predicate. By supplying 
tins omission, Hamilton has indicated four additional forms. 
Thus, to take All X is Y : all men are fallible. Y may 
mean some Y or all Y; some fallible beings or all fallible 
beings. There are then two forms :— 



I 



HAMILTON'S QUANTIFICATION. 87 



(1) All the Xs are some (a part) of the Ys; all men aro 
ome (a part of) fallible beings. This is what is presumed to 
ie the meaning of the common form, where the quantity of the 
■redicate is not stated. As there is no assurance given that 
he Xs are all the Ys — that men are the whole of the beings 
hat are fallible — we must leave it to be understood that there 
re other Ys, other fallible beings, and therefore take for 
ranted only that men are among the fallible beings, whether 
here be others or not. Usually, we do not concern onrsolves 
nth this farther enquiry ; it is enough for us to know, on a 
•articular occasion, that a certain man, or a number of men, 
re fallible, or that a certain substance is poisonous, without 
etermining whether others besides those in hand have the 
ame quality. This last is a distinct and superadded enquiry, 
iseful in particular situations, but not in all, nor even in the 
aajority of instances. The fact is valuable to know that 
wines are stimulating or intoxicating/ whether or not they 
nclude the whole of the stimulants. It is a farther discovery, 
taving a separate utility, to find that there are stimulants 
>esides wines. The common form is suited to the first case ; 
he quantified form — all wines are some stimulants, there are 
»ther stimulants besides wine— is suited to the second case. 

On the strict Logical sense of 4 some/ — some at least, and 
t may be all,— the quantified form i all X is some Y' is the 
iame as the unquantitied form 'all X is Y/ There is merely 
his difference that in the quantified form, attention is called 
o the circumstance whether there be more Ys than are Xs ; 
n the common form, no question is raised or even suggested 
is to additional Ys beyond the Xs. If ' some ' were inter* 
)reted in the more familiar meaning * some at most,' which it 
s apt to be, the particular quantification would not give the 
neaning of the unquantified form. 

It will be seen, in the account to be afterwards given of 
3oole's Logic, that he finds it necessary to express, by a sym* 
)ol, that the predicate of affirmative propositions is taken 
)nly in - part of its extent. 

(2.) With the predicate made universal, the form A becomes 
All X is all Y;' there are no Ys but the Xs. Such is not 
i usual form of predication. In the great mass of positive 
ifnrmations the predicate is larger than the subject, includes 
t and other things besides : l the coin of the realm is metallic / 
here are many things made of metal besides coin. ' The stars 
ire heavenly bodies/ but not exclusively so. 

To exemplify this kind of proposition, there are offered such 



88 EXTERNAL FORM OF PROPOSITIONS. 

instances as these ; — * Chloride of sodium is common salt,' 
which means, there is no chloride of sodium but what is 
common suit. But these terms are co-extensive only because 
they are synonymous ; they are two names for the same thing. 
Defining propositions must be co-extensive. 

As an example taken from real propositions, we may have 
this — ' All equilateral triangles are all equiangular triangles ;' 
for there are none equilateral but are also equiangular. Such 
cases are not frequent even in the deductions of Geometry, 
where the propositions affirm prop r ia> and not concomitance. 

There are a few cases of unique properties furnishing propo- 
sitions where the subject is. as large as the predicate. i Mercury 
is a liquid metal ' is known to be ' all mercury is all liquid 
metal.' In sack instances, it is usual to note the fact, that 
subject and predicate are co-extensive in the language used ; 
as by saying, mercury is the only liquid metal ; there is no 
metal liquid at common temperatures but mercury. Being an 
exceptional predication, it receives exceptional notice. Of a 
similar nature is Hamilton's example, * All rational is all 
risible ;' we should say, fc only rational beings are able to laugh,' 

In the more general conjunctions, or concomitance of dis- 
tinct qualities, it is exceedingly rare to find a proposition where 
subject and prodicate are co-extensive. Only one unequivocal 
instance can be suggested at the present time, namely, the 
proposition, ' all matter gravitates ;' the meaning of which is 
that the defining property of matter — Inertness — is always 
accompanied with the attraction of gravitation. Now, these 
two attributes are co-extensive, and yet distinct ; all matter is 
all gravitating things ; there is nothing devoid of inertia, and 
yet possessing gravity. Even here it may be said, that although 
we can easily suppose inertia without gravity, we cannot easily 
suppose gravity without inertia. 

Polarization and Double Refraction are co-extensive pro- 
perties. 

Mr. De Morgan, as will be afterwards seen, calls the form a 
complex proposition, being tantamount to two propositions- 
All X is Y, and all Y is X. 

Mr. Mil] makes substantially the same criticism on Hamil- 
ton s Quantified forms. Whatever can be proved from " all 
A is all B, can be proved in the old form from one or loth of 
its elements, All As are Bs, and all Bs are As. < Whatever can 
be proved from « Some, and only some, A is some (or all) B," 
can be proved m the old form from its elements. Some As are 
bs, some As are not Bs, and (in the case last mentioned) all 



HAMILTON'S QUANTIFICATION. 89 

are As.' (Mill's Hamilton, chap. XXII). To gay 'All 
Philosophy is all Poetry' is to affirm these two proposi! 
Poetry is Philosophy, and Philosophy is Poetry. 

The Particular Affirmative, I, has two forms, when the 
quantity of the predicate is supplied:— Some X is some V, (tho 
understood form), some X is all Y : ' Some planets are some 
celestial bodies;' 'some mortals are all men.' The second is 
the new or additional form. Its best justification is the cir- 
cumstance that, under the common form, we lose predication 
in converting a universal affirmative : thus, All X is Y, all nun 
are mortal, become, some YisX, some mortal beings are men, 
meaning some X, some men, whereas we are entitled to say all 
X, all men. 

These two additional affirmative forms liave been admitted 
by some logicians, as Thomson (Laws of Thought) and Spald- 
ing ; and have been made the basis of an extension of the 
syllogism. The universal affirmative — All X is all Y — is sym- 
bolized by U (Thomson) and by A 2 (Spalding). The par- 
ticular affirmative with, universal predicate is Y (Thomson), 
l a (Spalding). 

The additions made by Hamilton to the negative forms, 
E, and O, have not been received by any other logician. In 
E, ' no X is Y, ' no men are gods/ both subject and predicate 
ire universal ; there is total and mutual exclusion ; no one 
)f the class men is identical with any one of the class god ; the 
3oincidence of a man with a god is denied seriatim. The pre- 
dicate here is quantified universally. We may, however, state a 
:orm where the predicate is particular ; ' no X is some Y,' ' no 
nen are some animals,' no men are to be found in a certain 
3lass or species of animals; there are classes of animals that 
3ntirely exclude men. If the ' some animals ' could be speci- 
ically defined, as quadrupeds, fishes, &c, the proposition would 
revert to the common form. 

In the Particular Negative, 0, ' some X is not Y,' the sab- 
ect is particular, and the predicate universal. ' Some Xs are 
lot to be found among the Ys ;' ' some men are not any 
Europeans, are not to be found among Europeans ;' 4 soino 
leavenly bodies do not shine by their own light.' 

Now, particular quantity may be assigned to the predicate; 
vhich would then be, some X is not some Y ; some of the Xs 
lo not occur among some of the Ys. Some men are not to bo 
bund among some of the mammals. If * some of the mam- 
nals,' could be rendered specific, as the ' carnivorous quadru- 
)eds, ' the thick-skinned quadrupeds/ we should have the old 



90 EXTERNAL FORM OF PROPOSITIONS. 

form of 0. In answer to the objection against the new form 
thai it is never practically realized, Hamilton contends that ii 
18 the form wherein, exclusively, we declare a whole of any kino 
to l»- divisible. Thus, in dividing the genus 'soldier/ wt 
should say to ourselves — "some soldier is not some soldier. 
\'nv some Soldier is (all) Infantry, some Soldier is (all) Cavalry, 
<fce. ; and (any) Infantry is not (any) Cavalry.' ' 

Do Morgans Enumeration of Propositions. 

0. With a view to exhaust all the possible modes of pre- 
dication, there needs to be a thorough-going expression oi 
contraries. 

According to the true view of contrariety, as given by De 
Morgan, the negative is a remainder, gained by the subtraction 
of the positive from the universe ; the negative of X is U — X, 
and may be symbolized by a distinct mark x ; whence X and 
x are the opposites under a given universe ; not-X is x, and 
not-x is X. For, Some Xs are not Ys, we may substitute, 
Some Xs are ys ; and so on. 

We have now, instead of the two terms X, Y, the four 
terms X, Y, x, Y. Hence, in room of the one couple, X, Y, to 
be given under the four forms of predication — A, E. I, O — we 
have no less than four different couples — X, Y ; X, Y ; x Y; 
x, Y. Every one of these may be stated, as A, as E, as I, or 
as 0. Consequently there are sixteen possible arrangements. 
On examination, however, eight turn out to be repetitions of 
the other eight. 

We may exhibit the sifting operation thus : — Take A, or 
universal affirmation, and express all the four couples accord- 1 
ingly. 

(1) All X is Y (the usual form) 

(2) All X is Y (not-Y) 

(3) Allx (not-X) is Y 

(4) All x (not-X) is y (not-Y) 

The second— All X is Y (not-Y)— is identical with E, in the 
old scheme — No X is Y. 

The third— All x (not-X) is Y, is the same as no not-X is 
not-Y ; nothing is both not-X and not-Y ; everything is either 
X or Y. No not-mind is a not-matter ; everything is either 
nmid or matter. This is a new form. It means that every- 
thing is either in X or in Y (or in both). 

The fourth— All x (not-X) is y (not-Y), (all not-mortals are 
not-men), is the same as All Y is X, a new form, so far, that 
the symbols are transposed. 



DE MORGAN'S PROPOSITIONS. <,j 

Again, putting the four couples through particular affirma- 
tion (1) :— 

Some X is Y 

Some X is y (not-Y) 

Some x (not-X) is Y 

Some x (not-X) is y (not-Y) 
The first being the common form; the second is the common 
particular negative. The third, ' Some not-X is Y,' may be 
transformed into ' Some Ys are not Xs,' or ' All Xs are not Some 
Ys,' in which shape it is received among the additional forms. 
The last ' Some not-X is not Y ;' 'some things are neither Xs 
:ior Ys ;' all the opposites of X are opposites of Y. infantry 
is neither cavalry nor artillery ; the negative of X (cavalry) is 
Me negative of Y (artillery), that is, infantry. 

The same method pursued with universal, and with particu- 
lar negation, completes the survey, and also yields a new 
form, already quoted, 

Some Y is not X 
►vhich, like the form — All Y is X — is merely the transposition 
>f the letters in O. The author has special reasons for 
Deluding these two varieties among propositional forms. 

Thus, then, in addition to the old fundamental forms, A, I, 
E, 0, we have these four : — 

(1) Every Y is X 

(2) Some Y is not X 
ivhich are A and O, reversing the terms. 

(3) Everything is either X or Y 

(4) Some things are neither X nor Y 

These last are a contrary couple of Disjunctives, added to the 
bur regular forms, which are all Categorical. 

The author next adverts to the compatibility or incompati- 
)ility of these various forms. There are three alternatives. (1) 
The separate individuals may be such as cannot exist together. 
2) They may be such as must exist together. (3) They may 
jxist either with or without each other, in neutral concomitance. 
.t is evident, for example, with regard to the old forms that A 
;annot co-exist with E, or with ; if every X is Y, it cannot 
>e true, either that no X is Y, or that some X is not "i . 
\-gain, if A exists, I must exist : and so with E, and ; the 
articular is involved in the universal. Lastly, the particulars 
. and O, mayor may not exist together: they are neutral 
concomitants; 'some men are wise,* and 'some men are not 
vise.' [Substantially the statement of the Opposition of Pro- 
positions.] 



92 EXTERNAL FORM OF PROPOSITIONS. 

From this, the author proceeds to define what he terms t 
comph rition; ' one involving within itself the assertiot 

op denial of each and all of the eight simple propositions. 
Thus supposing X and Y to be such that none of the foui \ 
universal are°true; then all the four particulars are true, 
This is one case, called a complex particular. Another case is • 

Pju.se one of the universals true; then five others art 

Bettled, either by affirmation or by denial: and there are twe 

concomitants, which however, are contradictions, so that onlj 

> true. Of this generic character, there are six modes 01 

Conns ; one of which has an especial interest. 

The case is this, Let A (the old form), 'Every X is T ' be 
true. Then E and 0, are denied, and I, is included (of the 
old forms). Of the four new forms, the neutral concomitant 
is 'Every Y is X ' : these may co-exist, and when taken to- 
gether make the complex proposition— Every X is Y, and 
every Y is X: in other words, X and Y are co-existent, or 
identical. Now this is Hamilton's Universal Affirmative, with 
universal quantity in the predicate. All Xs are all Ys. So 
tint, in De Morgan's view, that form has no claim to be a i 
simple or fundamental propositional form ; it is a compound 
or complex proposition, derived from the simple forms, by the 
process now described. He supports this view, by the farther I 
allegation, that the proposition in question does not admit of a < 
simple denial, as every proposition of a fundamental kind 
should : it is contradicted either by ' Some Xs are not Ys' 
and by ' some Ys are not Xs ' ; that is, by the disjunction ; 
1 either some Xs are not Ys, or some Ys are not Xs ' ; and it i 
is not necessary to determine which, so that the contradictory 
is ambiguous or undecided. 

Opposition of Propositions. 

^ 10. legation in the full sense is exhibited by opposing a 
Universal Affirmative to a Universal Negative— A to E, 
as 'all men are wise, no men are wise/ This is called, in 
JC| the opposition of Coktbakies. 

^ Contrariety, in this sense, is the setting up of a Universal 
Negative, against a Universal Affirmative, or a Universal Affir- 
mative against a Universal Negative : All X is Y, no X is Y; 
'all the ship's crew perished/ ' all the ship's crew survived/ 
In point of extent, this is the largest, the most sweeping and 
thorough negation, that can be advanced. The amount of 
knowledge required for such a denial, is at its maximum. It 



OPPOSITION OF CONTRARIES. 93 

is not often that, in dissenting from a Universal Proposition, 
we are able to substitute the opposite universal. We may 
loubt the truth of the affirmation 'all stars twinkle ; ' but wo 
cannot carry our denial to the length of Universal Negation- 
no stars twinkle.' Rarely does any informed person, in id* 
rancing a universal proposition, go so fur wrong, that the 
truth consists in the opposite universal. 

There is the appearance of complete contrariety in the op- 
posing views of the Immortality of the Soul. Christian 
• the souls of all men are immortal ; ' Buddhists and others 
1 no men's souls are immortal.' This, however, is one of the 
instances, where a universal is alike proved or disproved upou 
an individual case. 

In small matters, total contrariety is frequent enough. The 
assertion may be made — * Ail the voters were bribed,' and 
may be met with the universal denial — ' no voters were bribed / 
which is felt to be the strongest denial that can be given. 

Of this opposition, it is remarked, that both cannot be true, 
but both may be false. ' All men are wise • and f no men are 
wise/ cannot be both true ; the intention of the one is to de- 
clare the other to be false ; between the two, there is a con- 
tradiction in terms. Yet it is possible that neither may be 
true, that both may be false. The truth may be neither the 
one, nor the other, but something betwixt the two sweeping 
uuiversals ; as, that some men are wise, and some not wise. 
Total contrariety, or complete negation, thus leaves room for 
a middle assertion^ 

It is farther pointed out in regard to this opposition, that 
the opposed propositions differ only in quality ; the one affirms, 
and the other denies, of the same quantity, that is to say, the 
universal, 

11. A Negation may consist in opposing a Universal Affir- 
mative to a Particular Negative— A to O, or a Universal 
Negative to a Particular Affirmative — E to I. This called 
the opposition of Contradictories. 

Instead of ' All men are wise/ ' no men are wise,' we may 
have the opposing couple, ' All men are wise/ ' some men are 
not wise; A and O. So, 4 No voters were bribed' (E), is 
opposed by ' Some voters were bribed ' (I). Such is contra- 
dictory opposition. 

Of this opposition (as with contraries) both cannot be true ; 
but farther, both cannot be false, or if the one be false the other 
must be true, and if the one be true, the other must be false. 



94 EXTERNAL FOKM OF PROPOSITIONS 

There is not, as with contraries, an intermediate supposition; 
there is no middle ground. Either ' all men are wise/ or 

me men are not wise ;' either ' no voters were bribed ;' or 

tae voters were bribed.' The two opposites are so related 
that we must choose one or other. Hence to this kind of 
opposition belongs that principle first signalized by Aristotle, I 
and ever since regarded as a primary Law of Thought — the 
Law of Excluded Middle. 

It is farther noticed, that in contradictory opposition, there 
is change both in the quality, and in the quantity of the opposed <j 

it ions; while one is affirmative and the other negative I 
the one has universal, and the other particular quantity. This I 
circumstance, however, instead of increasing, diminishes the 
contrariety. The change from universal to particular quantity \ 
abates the force of the opposition of quality. 

The application of perhaps the strongest negative word in ' 
the language, — contradiction — to this kind of opposition calls i 
for some comment. In common speech, the person that could, I 
in reply to the charge — 4 All the voters were bribed,' maintain j 
4 No voters were bribed,' would be held to have contradicted 
that charge in the most thorough-going way. While the de- 
claration 'some voters were not bribed' wonld be regarded as i 
a contradiction, the declaration — * no voters were bribed P 
would be held as a contradiction in a still higher degree. The 
word 'contrary would be thought too feeble for universal denial. 
It is apparent, that the logical contradictory, as now defined, 
denies much less than the logical contrary; indeed, denies so i 
little, that it excludes the possibility of a smaller denial ; it is 
the minimum of denial. For, whereas the affirm er boldly com- 
mits himself, for example, to the broad universal ' all men are 
wise,' the denier, timid and shrinking, ventures only upon an 

ption to the sweep of the rule ; he will not say, 'no men 
are wise,' which would be in common speech the flat contra- 
diction, the thorough negation ; he merely says some men are 
not wise; he denies so little, as to leave no room for any one to 
deny less. He takes ground so limited, so humble, as to ex- 
clude any more limited, more humble opponent. His * some' 
commits him only to the fact of taking an exception. It 
may mean only one; which of course would be an 'excluded 
middle/ tor who that challenged the assertion ' all men are wise ' 
could say less than 'owe man is not wise ? ' It is shaving the 
universal affirmative by the breadth of a hair thatcannot be split. 
I he employment of the stronger term for the smaller oppos- 
tion, is explicable thus. Aristotle, in dividing propositions 



OPPOSITION OF CONTEADIUTOIUES. 

according to quantity — as universal and partial, — put prcat 
stress upon the difficulty in establishing, and the fociii 

subverting, a universal, whether affirmative or v. 
task of the alllnner is hard, he has to secure every indii i 
instance ; the task of the denier is easy, lie has but to de 
one. If it were necessary, with a view to impugn a nniv 
proposition, to establish an opposite universal, the difficul 
disproving an unsound generalization would be often in 
able. This, however, is not required. A single oppi 
is enough. A hole in a ship's bottom sinks her as Bai 
she were torn plank from plank. It is this / for 

>of that makes the importance of the limited contradictory 
affirmation. It can be more easily procured than the full 
contrary, and yet it is equally effective. It possesses tlio 
imposing circumstance of securing great ends by small mi 

There are certain cases where the contrary and the contra- 
dictory are the same thing. The first is when the proposition 
is singular or individual : 'John is here' — 'is not here,' 'The 
world was created in time/ i The world is eternal,' There is 
no middle ground in such assertions as these. 

Another case is where a generality stands or fall 3 by an 
individual case, as iu Laws of Causation. A single unambigu- 
ous observation (under what is called the Method of Difference) 
wiil prove Cause and Effect. If a new metal is discovered, 
and fused on one single occasion at 1100 deg. Fah., we may 
affirm generally that the same temperature will always fuse the 
metal. Here contrariety and contradiction are the same. 
The metal either is or is not fused at that temperature. The 
Uniformity of Nature prohibits the middle supposition, that 
some portions of the metal may be fused and some not. 

These remarks serve to explain the use of the Law of Excluded 
Middle, by Sir W. Hamilton, in regard to certain questions, such 
as the Infinite Divisibility of Matter, Free-AVill, the Eternity of 
the World. 'Matter is divisible,' 'matter is not divisible '—are 
contraries not contradictories ; there may be a middle position — 
* some matter is divisible '—making them both false. But Hamilton 
must be understood to assume that Matter, either is a «iw< 
subject, or is homogeneous to such an extent that what is true of 
one portion must be true of all, and consequently that the opposi- 
tion above specified comes under contradictory opposition, which 
is governed by the Law of Excluded Middle. Accordingly, ho 
maintains that of the opposite alternatives— matt ihle, 

matter is indivisible; the will is free, the will is necessitated— 
one must be true and the other false. 

A farther logical convenience supposed to attach to the con- 
tradictory form 1 is the substitution, tor the denial of a universal, 



96 



EXTERNAL FORM OF PROPOSITIONS. 



of the equivalent., and corresponding affirmation. When A is 
denied, then, in that very act, O is affirmed. It being nntrue that 
4 All men are wise,' it must be true that * Some men are not wise/ 

The Contrary and the Contradictory are the only important 
forms of opposition. It is usual to add another variety, that 
between a Particular Affirmative and a Particular Negative — 
1 and — • Some men are wise/ ' some men are not wise.' 
So imperfect is this opposition, that there need not be any 
contrariety between the two forms. They are compatible, and 
are often both true. All that can be said of them is, that they 
can not be both false; if it is false that some men are wise, it 
cannot also be false that some men are not wise. But as the 
one predicate may relate to one set of men, and the other predi- 
cate to a different set, there is no real contrariety ; frequently 
the two propositions together give the exact state of the case. 

The name * sub-contraries ' has been given to these opposites. 
According to Hamilton, they were brought forward merely as 
completing thelogical diagram, called the ' Square of Opposition.' 

For the explanation of the diagram, it is farther to be re- 
marked that the relation (which cannot be called opposition in 
the strict sense) between Universal and Particular — A and 
I, E and 0, is called snbalternate, or subaltern, the relationship 
of subordination. There is a sufficiently obvious propriety ia 
60 designating it. 

Common Square. 
A Contraries. E 




Sub-Contraries. 



SQUARE OF OPPOSITION. 



97 



Mr. I?a Morgan departs from this square on certain points. 
Regarding the words * contrary ' and 'contradictory' as tho 
same in meaning, he drops ' contradictory/ and applies 4 con- 
trary ! to the old meaning of contradictory, that is to tho 
diagonal opposition, A — O, E — I. The opposition oi tho 
Universals, A — E, he proposes to style sub-contrary; and tho 
opposition of the Particulars, I — 0, which he retains, ho calls 
super-contrary. 

If we were to introduce any innovation of this nature, founded 
on the identity of contrary and contradictory in common speech, 
there would be a greater seeming propriety in the invering of 
Mr. De Morgan's designations. The opposition of the Uni- 
versals A and E — is full contrariety ; the opposition of the Uni- 
versal to the Particular of opposite quality (however elFective 
as a logical instrument) is still but partial contrariety, or 
subaltern contrariety, and would better suit the name i sub- 
contrary .V A* — 0, E — I. The opposition of the particulars I 
and O does not, so far as can be seen, need any descriptive 
name. If it did, 'super- contrary ' might be taken. 

The supposed square would stand thus : — ■ 

A Contraries. E 




I 

This form is the following out of the view already taken of 
the imperfect negation of the so-called contradictories. It 
is also so far in harmony with the scheme of the diagram 
(borrowed from the Paralleligram of Forces), a superficial 
harmony founded on a deeper propriety. Thus, A E, being one 



93 



EXTERNAL FOKM OF PROPOSITIONS. 



i!df of the square, and the line of the snbalterns, A I, being 
lide adjoining; the composition of these two, into the 
diagonals, A— O, or E — I, yields subaltern contraries, contracted 
into suh-amtraries. This is not a mere accidental coincidence 
of laftHTMge ; it is the expression of the fact that snbaltern or 
subordinate contrariety, is a subordinated, narrowed, or partial 
form of contrariety ; a whole is opposed, not by a whole, but a 
part ; a aniversal met, not by a universal, but by a particular ; 
giving a diagonal or oblique contrariety, instead of a full or 
total contrariety. 

This is different from the common square, as well from the 
two others given above. Aristotle uses the diagonal for the 
full contrary opposition of the two universals A and E. The 
contradictories, or sub-contraries, A-0, E-I, are the sides (be- 
tween right and left). There is no opposition indicated between 
A and I, E and ; and the second diagonal is left blank, in- 
asmuch as I and 0, are not proper contraries. This square 
has the diagrammatic property of representing the strongest 
contrariety by the longest line, the line also that bisects the 
figure ; from which arrangement arose the emphatic phrase 
diametrical opposition, to signify the thorough opposition of 
the universals. 

Aristotle's Square. 

A Contradictory. 




Contradictory 



NECESSARY AND CONTINGENT. 99 

Modal Projiosi/ions. 
12. Since, in common speech, Propositions often o 

in a qualified or modified form, a class was constituted )>v 

Aristotle for such cases, under the name of Mo pal 
positions ; the unqualified forms being called the j 
forms. 

If we were to say that, in Geometry, ' the conclusion n 
sarily follows from the premise?/ the affirmation would ho 
called Modal ; it lays down a truth and farther desigmr 
as a necessary truth. The contrast of necessary is tontin 
which is also a modal ; the propositions of physical science are 
looked npon as not necessary, but contingent; the facts might 
have been arranged otherwise. So that besides affirming that 
oxygen combines with hydrogen, we might call it a * contin- 
gent' doctrine or statement^Other generic forms of modal- 
ity, included by Aristotle, are the possible, and impossible ; both 
which may qualify propositions. He reduces these four forms 
to two, — necessary and contingent. He was supposed also to 
have taken in trite and false among the kinds of modality. 
Although this is doubted by some, there would be no reason 
why they should not be included. So, probability and impro- 
bability might be likewise admitted. Subsequent logicians 
extended the species of modality to qualifying adjectives or 
adverbs, as ' the white man runs,' ' he runs quickly. 9 Again, 
the qualification of time is an important fact entering into 
many propositions ; he ran yesterday ; he continues running. 

That such propositions are frequently to be found is obvious. 
By Hamilton and the stricter of the formal logicians they are 
excluded from Logic. They clearly do not belong to the narrow 
Formal or Syllogistic Logic. They have reference to the matter 
and not the form of predication. They are included in the more 
comprehensive Logic sketched in this work ; and we can 
easily assign their proper position in the enlarged scheme 
Propositions qualified as Necessary, first give an affirmation, 
and secondly, declare that such affirmation belongs to the class 
of necessary truths, whatever these may be ; whether this 
be true or false depends on a comparison of the marks of the 
( class ' necessary truths,' or the connotation of the word 4 i 
eary,' with the affirmation in question. The case falls under 
Deductive Evidence, not formal, but material, like the inter- 
pretation of Law. The same remarks apply to Contii 
Possible, and Impossible propositions. With regard to Vrvba^ 



* 



apossible propositions 



100 lMrORT OK MEANING OF PROPOSITIONS. 

ftflifo as a modal, a reference would be made to the branch of 

Induction treating of Probable evidence, 

positions qualified by present, past, or future time, or in 

cs of the verb besides the present viewed as the 

universal tense, may be treated as compound propositions; 

ting first a fact, and then the time of its happening. 

Another view of these, suggested by Mr. Mill, is to associate 

the tense with the copula. 

In the Appendix (Explanation of Tekms, Modals) will be given 
the usual statement of the Opposition of Propositions, as applied 
t » NYccssary, Impossible, and Contingent matter. It is withheld 
from thu Text, as being an irrelevant and useless complication. 

IMPORT OR MEANING OF PROPOSITIONS. 

13. For laying out the divisions of the Inductive Logic, 
it is requisite to classify propositions according to their 
Impokt or Meaning. 

Although the special meanings of propositions are as various 
as human knowledge, there are certain highly generalized 
meanings, pointing to difference of Logical Method. 

14. To the question, what is, in matter or suhstance (as 
contrasted with/orm), the meaning of a Proposition, Hobbes 
answered that, in a proposition, the predicate is a name for 
the same thing as the subject is a name for. 

Thus, ' Aristides is just ' is a true proposition if 'just' be 
the name of Aristides. * Men are gods ' is false, because 
* god ! is not a name for man. 

This is true, but not the whole truth. The theory is correct 
so far as it goes, but it does not reach to the final import of 
predication. Hobbes did not advert to the real meaning, which 
is found in the connotation of class names. When we say, 
4 Aristides is just,' the preliminary question arises, how came 
the name 'just' to be applied to Aristides? When the 
word was first determined on, people knew nothing of Aris- 
tides. What they knew was the agreement of a certain 
number of persons in a peculiar feature of conduct ; to that 
Agreement was given the name 'just.' Any one in after times 
found to have the agreeing feature, succeeded to the name; 
and the meaning of the proposition as regards Aristides is 
that he resembled a number of persons that went before him, 
in a certain point where they resembled one another ; and on 



THEORY OF MEDICATION. 101 

account of which, they were named 'just.' In one view 
therefore, the proposition in question is an affirmation of 
mess ; but that fact must enter into every proposition asserting 
participation in a community of attributes. More char 
of the case is the feature of co-existence ; the co-existence of the 
man Aristides with the quality named 'just.' Two things are 
mentioned; and these two things are united in predication 
by declaring their co-existence in one subject. Whether this is 
a typical or representative instance, Will be seen, alter a fuller 
examination of particulars. 

15. A second theory, sharing in the same defect as the 
foregoing, is that Predication consists in referring so'riuthing 
to a class, — placing an individual under a class, or one 
class under another class. 

When we say 4 the planets are round,' on this hypothesis 
the meaning would be, ' the class planet falls under, or is 
enrolled in, the class round;' 'Neptune is a planet,' Neptune 
is in the register of bodies named planets. Or, negatively, 
* men are not gods,' men are not to be found in the list of the 
gods. This is both inadequate and incorrect. It confounds 
the connotation of a name with its denotation ; the class 
attribute, which is elastic and indefinite, with the class as 
supposed to be an aggregate of definite individuals. The 
meaning of a general name is as extensive as the things that 
possess the attribute; although a certain number of known 
individuals may be recognised as a group, or class, correspond- 
ing to the name, the class must ever remain open to new 
individuals. We have a general name ' sea,' which is also a 
class name, in the narrow sense. The individual seas of the 
globe are enumerated in geography ; but these are not exclu- 
sive. We could not refuse the name ' sea ' to a newly discovered 
individual, because it is not in the old list; if it possessed the 
common features, we should give it the name at once, and 
write it down in the list afterwards. Most general names 
have no lists or registers of individuals ; we have no exhaust ive 
tables of round things, of stars, of coal strata, of whales, or of 
human beings. We have merelv points of agreement, defining 
marks ; in other words, a meaning or connotation to eaeli 
term; the correspondence with this rules the application of 
the word, or the truth or falsehood of the proposition asserting 
that any individual is round, is a star, and so on. 

In forming a class, we do not, as in forming a society, 
enroll certain definite individuals, and decide eaeh ones 



102 IMPORT Oil MEANING OF PROPOSITIONS. 

pretensions by referring to the roll. We indicate an attribute 
or attributes, and test the individual by the presence or the 
nee of the attributes. 

1(>. There are two ways of arriving at the highest gener- 
alities of Predication. One is a sufficiently wide examina- 
tion of actual propositions in the detail. The other is to 
refer to the classification of ' Narneable Things/ The two 
modes should confirm each other. 

By an examination of propositions in detail, we should soon 
had many of the kind already noted as affirming Co-existence; 
the co-existence of two things, or facts, or two properties. 
4 .Man is mortal,' is the co-existence of humanity and mortality. 
4 The fall of the barometer is a sign of rain,' is the concurrence 
of the two facts, the fall of the barometer and rain. 

AVe might then turn from co-existence, to its contrasting 
property, < Succession/ and enquire whether any propositions 
are made up of two or more things affirmed to happen in 
succession. "We should find many such. 'The wind raises 
the sea/ ■ the sun is the cause of vegetation/ * Caesar subverted 
the Roman Republic/ might all be interpreted as affirmations 
of succession. Speaking generally, wherever thei^e is produc- 
tion, causation, or change, there must be succession ; one state 
of things is followed by another state of things. In cause 
and effect, which is a very wide department of human enquiry, 
there is understood to be succession ; something called a cause 
is followed by some other thing, called an effect. 

We have seen, farther, that in predication, there is involved 
the declaration of Likeness and Unlikeness. This contrast, 
however, is a universal fact inseparable from predication ; the 
very basis of cognition is laid in Difference and in Agreement. 
But there are certain cases where the specializing point of a 
proposition lies in likeness or unlikeness ; as in propositions of 
Number. • Twice two is four' is an affirmation of Equality; 
the test of its truth would be a test suited to ascertain equality 
or inequality. lb could not be brought under either co-exist- 
ence or succession in an easy or natural way ; it falls readily 
and fitly under agreement or disagreement in respect of 
Quantity. 

17. A reference to the classification of Narneable Things 
shows the wide compass of these three affirmations — 
Co-existence, Succession, and Equality or Inequality. 

Under Narneable Things (Appendix C), we find attributes 



PREDICATE OF EQUALITY. 103 

special to the Object, attributes special to tho Sttbj 
attributes common to both. The attributes common to both 
are Quantity, Co-existence, and Succession. We might, on tho 
strength of this enumeration, give, as universal forma o 
tion ; attributes of the Object, and attributes of the 
declared as agreeing or "disagreeing in Quantity, 
or as Successive. 

18. I. Propositions of Quantity include the who] 
the Mathematical sciences, and all the application 
number to quantity in every science and art. The precli- 
cation is equality or inequality. 

Thus, in Arithmetic, the addition and subtraction of num. 
bers, the multiplication table, and the rule of three, — which 
are the fundamental processes — are affirmations of agreement 
or disagreement in quantity. Three and four is seven ; live 
from nine leaves four; six times eight is forty-eight ; as two 
is to ten, so is six to thirty, — are affirmations of equality or 
agreement in numerical quantity. 

The propositions of geometry may all be resolved in like 
manner. The angle in a semi-circle is equal to a right angle. 
A sphere is equal in bulk to two thirds of the circumscribed 
cylinder. Two sides of a triangle taken together are greater 
than the third (Inequality). 

In Algebra, we need allude only to the extensive process of 
manipulating by Equations. 

In every art and in every emergency of life, occasion arises 
for measuring quantity, that is for declaring equality and in- 
equality, greater or less. Even when the quantity does not 
admit of numerical statement, as in shades of feeling and of 
human character, we still express and compare quantity ; we 
call one man more energetic, more far-seeing than another. 

19. It is the characteristic of the Sciences of Quantity 
to be purely Deductive Sciences. They have Inductive 
foundations like all the rest, but the chief labour attending 
them consists in purely deductive operations. 

This determines the Logical Method and the Logical Depart- 
ment of Mathematics. All that is peculiar in the science 
belongs to the branch of Logic named Deduction*. 

20. II. Propositions of Co-existenxr are of two k!: 

In the one kind, account is taken of Place ; they may be 
described as propositions of Order in Place. They icier 
purely to the Object, or Extended World. 



10 J: IMPORT OK MEANING OF PROPOSITIONS. 

The Object, or Extended Universe is a vast array of things 
distributed in space ; they are said to have place, or a mutual 
ionship as to extension. Thus, the stars are arranged iu 
I ial vault at detinite distances. Geography is a body 
of propositions of order in place ; an ocean, a mountain chain, 
a nvar — are described geographically as having local situa- 
tion with reference to other things; to these are applied the 
more purely mathematical or quantitative propositions of mag- 
nitude. 

Some propositions of Place affirm nothing beyond containing 
and contained ; they declare one thing to be either in or out 
of another thing ; — John is in the room ; the constellation 
Orion is in the northern hemisphere ; St. Helena is in the 
South Atlantic ; The British Museum contains the Portland 
vase. These may be called the more vague and indetermin- 
ate propositions of quantity. The degree of precision, in this 
case, depends upon the relative magnitudes of the container 
and of the contained. A thing affirmed to be in a house is 
better defined than a thing in a town, and not so well as a 
thing in a drawer. 

Another mode of giving order in place is to affirm close 
proximity. One thing outside another, but in contact^with it, 
has a detinite position, expressed by such forms as ' by,' ' by 
the side of,' ' close to, ? 'above,' 'beneath.' If there be an 
interval, a measured distance must be assigned. 

The more precise propositions of Order in Place are those 
that declare mutual position by numerical statements of dis- 
tance or extension ; to which form every fact of order in place 
might be reduced, if we had sufficient knowledge, and if we 
thought it necessary or desirable. Thus, the mutual position 
of the stars, in the sphere of the sky, is stated in terms of 
angular measurement ; the position of places in the earth is 
given by latitude and longitude, and also, if need be in linear 
distances. The determination and the expression of this rela- 
tionship, therefore, may be wholly referred to Arithmetic and 
Geometry. The precise statement of relative position is the 
peculiar province of Analytic or Co-ordinate Geometry. 

The description of all objects of the external world having 
parts, or a denned structure, demands propositions of Order in 
Place, according to some one of the foregoing methods ; as 
buildings, machinery, plants, animals, aggregates and collec- 
tions of objects. 

21. The second form of Co-existence may be designated 
Co-inherence of Attributes. 



CO-INHERENCE OF ATTRIBUTES. 105 

This is a distinct variety of Propositions of Co-cxisf<> 
Instead of an arrangement in place, with numerical into 
we have the concurrence of two or more attributes or powi 
in the same part or locality. A mass of gold contains, in every 
atom, the concurring attributes that murk the substance— 
weight, hardness, colour, lustre, incorrosibility, &c. An animal, 
besides having parts situated in place, has co-inhering func- 
tions in the same parts, exerted by the very same masses and 
molecules of its substance. Every blood corpuscle has a 
plurality of relations, indivisible and inseparable. 

The Mind, which affords no propositions of Order in Place, 
has co-inhering functions. We affirm mind to contain Feeling, 
Will, and Thought, not in local separation, but in commingling 
exercise. Every pleasurable feeling has its power of acting 
on the will and of impressing the memory ; all the attributes 
are joined in the unity of the mental being. 

A wide range of Scientific knowledge is comprised under the 
present head. The concurring properties of minerals, of plants, 
and of: the bodily and the mental structure of animals, are 
united in affirmations of co-inherence. The investigation of 
these concurrences, whether special or general, is a branch of 
scientific method, or of Logic, coming under Induction, al- 
though not the largest portion of the Inductive department. 

22. III. Under Succession, there are also two kinds of 
Propositions. By the first is predicated Order in Time. 

This is Parallel to Order in Place, under Co-existence. Many 
propositions consist in assigning the order and sequence of 
events, without intimating any closer relationship. The world 
being constituted on the principle of change, there is a serial 
order in its phenomena, which may be given in narration. 
Spring is preceded by winter, and succeeded by summer ; 
infancy is followed by youth. The treaty of 1815 followed 
Waterloo. 

The position of events may be defined by their close succes- 
sion. First the seed, then the ear, then the full corn in the ear. 
Henry VIII, succeeded Henry VII, and preceded Edward VI. 
A serial order being given, the position in the order is fixed 
either by contiguous events, or by a numerical position, as the 
sixth Earl. 

Here, too, as in order in place, the precise method con 
in the use of numbers. The flow of time being divided into 
years, months, days, hours, &c, the position of any occurrence 
is given by numbers and by fractions of numbers. Thia is 
merely another application of Arithmetic. In the complica- 



106 IMPORT OR MEANING OF PROPOSITIONS. 

tions of Astronomy, the element of time may require difficult 
algebraical formulae. There is, however, no^ new and distinct 
department of scientific enquiry involved in propositions of 
re sequence in time, however accurately they may be inves- 
tigated and recorded. 

23. The second mode of Succession, is that denominated 
Cause and Effect. The largest part of Induction is occupied 
with this department. 

Cause and Effect appears under the guise of Succession, but 
contains something beyond the sequences above considered. 
There is supposed to be a certain bond or nexus, a determining 
power or agency, whereby the one gives birth to the other. 
Propositions of Cause and Effect are such as these : — the ex- 
plosion of gunpowder propels a cannon ball ; the combustion 
of coal converts water into steam ; light is an agent of decom- 
position ; anxiety wears the constitution ; a good harvest 
mikes prices fall ; Demosthenes incited the Athenians against 
Philip. 

The Loeic of Induction is occupied first with propositions 
of Co-inheping Attributes ; secondly, and mainly, with pro- 
positions of Causation. Although the foundations of the 
science of Quantity are also inductive, yet so limited and simple 
is the induction, that it may be sufficiently noticed in the ac- 
count given of this department under Deduction and the 
Deductive Sciences. 

The foregoing is a modification of Mr. Mill's scheme of the 
Import of Propositions in the final analysis, conceived with the 
view of ascertaining the divisions of Logic. 

Mr. Mill enumerates five ultimate predicates, or classes of 
predications— Existence, Co-existence (including Order in 
Place), Succession, Causation, Resemblance. 

Apart from Existence, these are substantially the classes 
here adopted. Co-existence, as explained by Mr. Mill, com- 
prises Order in Place, and also the Properties of Kinds (Book 
III. Chap. XXII), which are given above under ' co-inhering 
attributes.' By Succession, is meant the looser successions 
included under Order in Time. The successions of Cause and 
Effect are given in a distinct and co-ordinate predicate— Causa- 
tion. ^ Under Resemblance, Mr. Mill indicates propositions ex- 
pressing the identity of the things discovered to be identical, 
as, for example, in classification ; but this underlies all pro- 
positions where there is generality, and does not mark off a 
scientific department. In the end, however, he gives as the 



EXISTENCE NOT A PREDICATE. 107 

special science of Resemblance, propositions of Quantity, or 
Mathematics. 

With regard to the predicate EXISTENCE, occurring in re: 
propositions, we may remark that no science, or department of 
logical method, springs out of it. Indeed, all such propositions 
are more or less abbreviated, or elliptical ; when fall 
they fall under either co-existence or succession. When we 
there exists a conspiracy for a particular purpose, we mean that 
at the present time, abody of men have formed themselves into 
a society for a particular object ; which is a complex aflirmat 
resolvable into propositions of co-existence and of succession 
(as causation). The assertion that the dodo does not ex 
points to the fact that this animal once known in a certain 
place, has disappeared or become extinct ; is no longer associated 
with the locality : all which may be better stated without the 
use of the verb * exist.' There is a debated question — Does 
an Ether exist ? but the correcter form would be this — ' Are 
beat and light and other radiant influences propagated by an 
etherial medium diffused in space ; ' which is a proposition of 
causation. In like manner the question of the Existence of a 
Deity cannot be discussed in that form. It is property a ques- 
tion as to the First Cause of the Universe, and as to the con- 
tinued exertion of that Cause in providential superintendence. 

EQUIVALENT PEOPOSITIONAL FOUMS — IMMEDIATE, OR 
APPARENT INFERENCE. 

24. Great importance often attaches to the equivalent 
modes of expressing the same fact, assertion or proposition. 
The transforming of one expression to another is so far aa 
aid to reasoning as to be sometimes termed ' Inference.' 

The enumeration of Equivalent Forms is as follows : — 
I. Universal and Particulars. 
II. Greater and less in Connotation. 
III. Obversion. 
IY. Conversion. 
V. Hypothetical Inference. 
VI. Synonymous Propositions. 

The first to the fifth, inclusive, are each conducted on a de- 
finite plan, admitting of precise rules. They are, therefore, 
the properly logical modes. The sixth, — Synonymous expn 
sion — is indefinite and various ; so that, although deserving of 
notice, it is not reducible to rule. 



108 EQUIVALENT PROPOSITIONAL FORMS. 

It will appear, in the course of the exposition, that in none 
of these cases is there Inference properly so called, that is to 

-, the transition from a fact to some different fact; there is 
merely the transition from one wording to another wording of 
the same fact. Hence, the designations ' Immediate Inference/ 
and 'Apparent Inference,' to distinguish the process from 
Mediate or Real Inference. 

C/iiversal and Particulars — Greater and Less in Denotation. 

25. A Universal Proposition and its constituent particu- 
lars being the same, there is no real inference, but a repetition, 
m saying All A is B, therefore Some A is B ; all men suffer, 
therefore some men suffer. 

A Universal Proposition is the summed up equivalent of 
many particular propositions, and has no force beyond, or apart 
from the particulars. Hence, when we state a particular case, 
we do but resolve the universal into its elements, and take these 
individually as they were before the universal was formed. ' All 
the houses of the street are newly built* is a mere summary or 
abbreviation of the separate enumeration — No. 1 is new, No. 2 
is new, and so on. To say * all the houses are new,' therefore 
1 No. 6 is new,' is not to make an advance in knowledge, but to 
fall back upon one of the constituents of the general proposition. 
The law of Consistency requires that whoever asserts a fact 
universally must be prepared to abide by it in each particular 
instance. A shopman advertises a number of articles at a 
shilling each ; the buyer, taking him at his word, chooses some 
one article, and puts down a shilling. 

Greater and Less in Connotation. 

26. In regard to the Connotation or Comprehension of a 
term, it is no inference to affirm the less after assuming the 
greater. 

When we say •' John is a man/ we say that he has each and 
all of the properties connoted by, or comprehended under 
' man.* It is no new affirmation, therefore, but merely unfold- 
ing in the detail what is already summed up in the aggregate, 

Bay John is a living creature, an animal, a compound of body 
and mind. Whoever is not prepared to admit these affirma- 
tions, should not declare John to be a man. 

In maintaining that 4 quadrupeds are endowed with mind/ 
we hold that they possess Feeling, Will, and Thought. It 






GKEATER AND LESS IN CONNOTATION. 109 

is, therefore, not a real inference but a mere iteration, to 
1 quadrupeds feel, ' * quadrupeds will.' 

When we affirm that a certain substance is arsenic, we B 
of it all the known properties of arsenic. It is an equivalent 
or identical proposition to say, 'the substance is poisonous, 1 

These affirmations of the properties of things in the detail 
have already come under our notice, as verbal, essential, or 
identical propositions. 

We must consider ourselves at liberty to join or disjoin the 
attributes of a thing, without real inference. Wo may 
either ' Socrates was wise, virtuous, and a martyr,' or ' Socrates 
was wise,' ' Socrates was virtuous,' ' Socrates was a martyr,' 
Given an aggregate or compound proposition, we may reduce 
it to its elements ; given a number of elementary propositions, 
we may compound them into one. The operation lies more in 
the grammar than in the sense. 

' Socrates was virtuous,' 4 there was one man virtuous,' — 
may be held to be a purely equivalent form. If we enquire 
into the meaning of the word Socrates, we find ' among other 
things ' that it means i a man,' ' one man,' and to say ' one 
man was virtuous ' is no new meaning, but a part of the ori- 
ginal meaning. So, after saying, i Socrates was virtuous ' and 
4 Socrates was poor,' there is no inference in saying t one man 
was virtuous and poor,' or i one poor man was virtuous.' This 
example has some importance in the theory of the Syllogism. 

Under the designation — Immediate Inference by Added De- 
terminants, the following case is given (Thomson's Laws of 
Thought) ; — * A negro is a fellow-creature ; therefore a negro 
in suffering is a fellow-creature in suffering.' This seems 
self-evident, but it is somewhat different from the other cases. 
It resembles the following mathematical inference : A = B, 
whence A -}- C = B -j- C ; which is not an immediate judg- 
ment, but deductively inferred from the axiom — 'The sums of 
equals are equal.' 

Even allowing the axiom of addition of equals for such a 
case, we must be cautious in applying it without regard to the 
matter, seeing that the same addition may not have the same 
effect upon both sides. * Beauty is pleasure ; hence beauty in 
excess is pleasure in excess,' is not a safe inference ; the quali- 
fication does not operate precisely alike upon both snbjec 

Diversion. 
27. In affirming one thing, we must be prepared to deny 
tho opposite: ' the road is level/' it is not inclined/ are 



110 EQUIVALENT PROPOSITIONAL FOEMS. 

not two facts, but the same fact from its other side. This 
process is named Obveiision. 

On the principle of Relativity, every statement has two 
sides, as a part of its nature : there is always something to be 
(umed when any one thing is affirmed. Whoever is ' wise' is 
k not foolish ;' we must grant both propositions or neither. In 
this we make no march, no addition to our knowledge ; the 
utmost that we do is to give completeness to the statement, 
there being usually an ellipsis or omission of the co-related 
fact. ' Tins end of the magnet is not the north end ; therefore 
it is the south end/ is no inference; if is is not north, it is, 
by necessary implication, south. ' I don't like a curving road, 
because I like a straight one/ is a childish reason, being no 
reason at all, but the same fact in obverse. 

To each of the four Propositional Forms, A, I, E, 0, there 
is an obverse form : — 

Thus, in A, 

Every X is Y; every man is mortal, 

We first ohvert ihe predicate, 

Every X is not Y ; every man is immortal, 

And next prefix the sign of negation. 

No X is not Y ; no man is immortal. 

So, all inert matter gravitates, no inert matter (not-gravitates) 
fails to gravitate. All gold is precious, no gold is (not-precious) 
worthless. All virtue is profitable, no virtue is (not-profitable) 
useless, devoid of utility. (Freedom of Trade tends to peace j) 
freedom of Trade averts war. All knowledge is usefuljllo 
knowledge is useless. 

To obvert I, 

Some X is Y ; some men are wise, 

Obvert the predicate, and prefix the sign of negation 

Some X is not not-Y ; some men are not (not-wise) foolish. 

Some stones are precious ; some stones are not (not-precious) 
worthless. Some virtues are burdensome; some virtues are 
not (not-burdensome) easy. 

For E, 

No X is Y, no men are gods. 

The obverse is, 

All X is not-Y ; all men are no-gods (excluded from the gods). 

No crows are white ; all crows are excluded from white 
things, are of some other colour than white ; or, if the universe 
of the predicate ' white/ be not colours, but white and black, 
'all crows are black.' 



OBVEHSION. X 1 1 

The rule here is the opposite of the rule for A : oh vert Die 
predicate, and remove Hie negative sign. 

The obverse of O, 

Some X is not Y ; some men are not is — wise 

Some X is not-Y ; some men are (not- wise) foolish. 

Some of the crew were not saved ; some were (not saved) I 

The rale still is ohvert the predicate, and remove the, 
rign, which is to change the quality of the proposition. 

The Universal affirmative with universal quantity in the pre- 
dicate, — 

All X is all Y ; all inert things are all gravitating things, is 
Dbverted to the same form as the obverse of A. 

No X is not-Y ; no inert things are found among things that 
do not gravitate. 

All equilateral triangles are all equiangular triangles ; no 
equilateral triangles are to be found among triangles with un- 
equal angles. All double-refracting bodies are all bodies that 
polarize light ; no double-refracting bodies are to be found 
among bodies that do not polarize light. 

The Particular Affirmative w r ith a universal predicate, Y has 
the same obverse as I. Some X is all Y : some mortals are 
all men. Some X is no not-Y ; some X is not to be found 
among not-Ys. Some mortals are not to be found among 
objects that are not men. There is a class or group of mortals 
that you will not discover among the brutes (Universe Ani- 
mals), among the plants (Universe organized bodies). 

Material Olversion. 

28. There are Obverse Inferences justified only on an 
examination of the matter of the proposition. 

From ' warmth is agreeable ' we can affirm, by formal ob- 
version, * warmth is not disagreeable, and not indifferent.' Wo 
cannot affirm, without an examination of the subject-matter, 
'cold is disagreeable.' 

There is a mode of inference, included by some logicians 
among Immediate Inferences, whereby we might say, i tho 
absence of warmth is the absence of an agreeable thing.' This 
granted, we are still a good way from * cold is disagreeable.' 
We must be able to say farther — ' the absence of warmth is 
the same as cold, and the absence of the agreeable is tho same 
as the disagreeable.' Bat we are not entitled to say this, ex- 
cept on a reference to the fact ; and such a reference teaches 
us that the absence of warmth may not be the same as cold, 



112 EQUIVALENT PROPOSITIONAL FORMS. 

and the absence of the agreeable not the same as the disagree- 
; tliero is a possible neutral state in both cases. Bat the 
ace teaches us that in an actual state of pleasure- 
warmth, thn sudden change to cold is also a change to the 
disagreeable. Whenever an agent is giving us pleasure in 
be abrupt withdrawal of that agent is a positive cause of 
On the faith of this induction, we can obvert ma- 
terially a large number of propositions regarding pleasure and 
, good and evil. If the sight of happy beings gives 
pleasure, we may infer, not by formal implication, but by 
rial or real inference, that the sight of unhappy beings 
i pain. The inference is a consequence of the laws of our 
)ility. While the sight of happy beings is giving us 
il pleasure, any sudden withdrawal or disturbance of that 
is a painful shock or revulsion. What is more, the 
nization formed to take pleasure in happy beings, is by 
that very circumstance formed to take pain at the sight of the 
unhappy. So we cannot take pleasure in opposing facts — 
praise and blame; we cannot become indifferent to the one 
without becoming indifferent to the other. 

From ' War is productive of evil,' we cannot say by formal 

obversion, * Peace is productive of good.' As before, 'the 

rion of war is the cessation of an evil,' and is therefore 

. in accordance with the law of our sensibility that the 

-n of a felt pain is a pleasure. 

It is a true inference, but not a formal implication, that if an 

upright minister gives public confidence, a shuflaino- minister 

causes mistrust. Provided the public confidence is° owing to 

the minister's uprightness, the replacing of that quality by its 

material opposite must produce the opposite of confidence. 

Ihe remark is sometimes made, 'government has great 

power for evil, and but little power for good/ KIgidly ex- 

amined, this is a contradiction. He that is able to do us a 

harm is able to refrain from that harm, and to make all 

the difference in our lot between our present tolerable condition 

and a condition of intolerable misery. The saying is true to 

xtent, that government interference, exerted for bad, could 

| more misery than the same interference, exerted for good, 

! cause happiness. s 

Mn° ld * mS an i im ? 1 ?\ does not necessitate 'heat keeps them 
So PnHffS ♦ m i Terence from the law of causation, we 
tl 1 aril Sa7, kee P aw ?7 the cold that kills, and, so far as 

formSnl- 1B f ? once ™ d . the a »imals wffl live! This is not 
lormal implication ; it is a certainty grounded on causation. 






SIMPLE CONVERSION. 113 

•Force compresses bodies/ does not justify * the withholding 
of force expands them. 1 We can say only, * the absent 
force leaves bodies in their uncompressed state.' This, in like- 
manner, is a material inference from causation. 

If 'knowledge is good,' we must concede the obverse, 
1 ignorance is bad,' but not by formal implication. Whatever 
amount of good, knowledge, as knowledge, is capable of doing, 
must be lost according as knowledge is withheld. 

Aristotle says, ' the beneficent man loves those he has done 
good to.' There is a familiar saying that may be given as a 
material obverse, c we hate those we have injured.' By the 
laws of our sensibility, the two facts are mutually involved ; 
although there are limitations that we learn by an induction 
from the facts. 

Conversion. 

29 The Logical doctrine of the Conversion of Proposi- 
tions is a case of equivalence. In Conversion, the Subject 
and the Predicate of a Proposition exchange places. 

The Proposition X is Y converted, becomes Y is X ; X is 
not Y, Y is not X ; men are mortals, mortals are men. 

The simple reversal of subject and predicate does not always 
give an equivalent form : i all men are mortals ' is not the 
same as * all mortals are men.' This arises from the circum- 
stance — taught us by our knowledge of things, and not 
discoverable by the examination of forms — that there are other 
mortals besides men. In all such propositions, therefore, a 
qualification must go along with the reversal of the terms. 

(1) In the forms E and I, the reversal of the order of the 
terms needs no qualification. Accordingly, this is termed un- 
qualified, or Simple Conversion. L No X is Y,' is commutable 
into ' no Y is X/ without alteration of meaning. If ' no men 
ire gods,' 'no gods are men; ' the proposition declares mutual 
Bxclusion or incompatibility, and we are at liberty to signify 
the exclusion from either side; X excludes Y, and Y equally 
3xcludes X. No crows are red ; no red objects are crows. No 
shemical combinations take place in fluctuating proportions ; 
ao combinations in fluctuating proportions are chemical. 

In I, ' Some X is Y,' 'some minerals are crystals,' we can 
say, by simple reversal, Some Y is X, some crystals are mine- 
rals. Some water is pure, some pure material is water. It is 
is when two areas cover one another partially ; the partial 
3oincidence is expressed from either side without change of 
signification. 



114 EQUIVALENT PK0P0SIT10NAL FORMS. 

2n a am] rsion of this nature, ' some ' has a different value 

propositions, unless the predicate and the subject are 

lh us, in the couple,— 4 Some men are dark-haired/ 

red beings are men,'-' Some men/ as compared with 

r fraction than * some dark-haired beings/ as 

i with ' all dark-haired beings.' 

(2) In converting A, the universal affirmative, * All X is 

Y/ 4 all fires give heat/ we have to qualify or limit the subject, 

some sources of heat are fires. There may be 

Yb besides the Xs, and other sources of heat besides fires ; 
bo that we must leave the possibility open, which would not be 

in simple conversion — (all Y is X, all sources of heat are 
To this qualifying conversion, logicians apply the de- 
signations Limitation, and per accidens. The Greek original of 
Aristotle was more descriptive, ica-ra pepo?, 'partitive * conversion. 
One of the recommendations of the thorough-going quanifica- 

cheine of Hamilton, is that it anticipates this necessity of 
qualifying the new subject. The proposition being expressed, 
in the first instance, as All X is some Y, or all X is all Y, as 
the case may be, the converse is Some Y is all X, or all Y is 
all X. ' All men are some frail things ; ' some frail things are 
all men. 

By far the most fertile source of purely syllogistic fallacies 
is the tendency of the mind to convert universal affirmatives 
without limitation. The usual form of the language, AH X 
is Y, unless we are specially put on our guard, is apt to be 
interpreted, as if X and Y were co-extensive ; in other words, 
we are disposed to regard it as justifying the simple conver- 
sion, all Y is X. The errors of syllogism to be afterwards 
] jointed out, under such names as Undistributed Middle, and 
Illicit Process, mostly grow out of this subtle error of conver- 
sion. When it is said, ' All powerful minds have large brains,* 
the hearer readily slips into the unlimited converse, ' All large 
brains indicate powerful minds/ This fallacy of conversion 

frequent occurrence ; and there is no more useful appli- 

Q of Logical forms than to warn against it. The best 
warning, however, consists in multiplying examples to show 
that, in universal affirmative propositions, the subject and the 
predicate are very rarely of equal extent ; and that, when 

are equal, it is usual to make known the fact by some 
iorm of language. 

instances are subjoined. ' 111 doers are ill dreaders/ 

not suppose that * 111 dreaders are ill doers ' ; there may 
many causes of dreading evil, besides having done evil 



CONVERSION BY LIMITATION. 115 

* All protestants exercise the right of private judgment ; 
do other persons besides ; hence we cannot say that who 
sxereises private judgment is a pro tes taut, 
i 'All beautiful things are agreeable ' ; beautiful things, how- 
ever, do not exhaust all that is agreeable ; there are more agree- 
able things than there are beautiful things. 

4 All virtue conduces to the good of mankind ;' it does not 
follow that whatever conduces to the good of mankind ia vir- 
tuous. * The good of mankind ' is a much wider meaning than 
virtue. 

'All the pleasures of the imagination/ says Addison, 'arise 
from the great, the uncommon, and the beautiful/ He must 
be supposed to mean that the sources of these pleasures are 
found among things that are great, among things that are un- 
common, and among things that are beautiful. But the classes 
'great' and 'uncommon' must contain many objects besides 
those yielding imaginative pleasure. If this is not the case 
with the 'beautiful,' it is because 'beauty' and 'imaginative 
pleasure ' are almost synonymous. 

When Sir G. C. Lewis remarks that ' Historical evidence 
requires contemporary registration^ he does not mean that con- 
temporary registration will of itself make historical evidence. 
This is one condition, but there are other conditions besides. 

The universal affirmative, when stated in Comprehension, or 
Connotation, — * the property A is accompanied by the property B,' 
' the attributes of man are accompanied by attributes mortal,' is the 
form least favourable to suggest a limited or qualified conversion. 
We are still more disposed than with the form of Extension, to 
convert simply ; — ' the attribute mortal is accompanied by the 
attributes of men.' Hence, for all the purposes of the Syllogism, 
the proposition in Extension is alone useful ; the fact being borne 
in mind, however, that the Extension is determined by the Connota- 
tion. 

(3) In converting O, the Particular Negative, (Some X is not 
Y, Some men are not Englishmen) a complex operation is 
necessary. Simple conversion — Some Y is not X, Some 
Englishmen are not men — does not apply. Two steps have to 
be gone through, first, obversion^ and secondly, simple conver- 
sion. 

Thus, by obversion, 

Some X is not-Y (something that is not Y), 

Some men are not-Englishmen (out of the class Englishmen). 

These obverted forms are Particular Affirmatives, and are 
therefore converted simply : — 

Some not-Y (something not Y) is X. 



116 EQUIVALENT PROPOSITIONAL FORMS. 

Some beings that are not Englishmen, are men. 
■ Some men are not wise.' By obversion, 

ae men are not-wise (foolish). 
By simple conversion, 

olish beings are men. 
Xhe given to this compound process are conversion 

um, or Contraposition. It might also be called 06- 

/ Conversion. . 

A similar operation may be performed upon A, the Universal 
Affirn » as to yield an equivalent negative form with 

I terms. The reduction of the syllogistic mood 
named Baroko, requires this operation. 
.us, 

All X is T, 
f Obversion, 

Ko X is not-Y. ^ 
which, b} r simple conversion (of E), is 
No not-Y is X. 
Or, 

All men are mortal 
No men are immortal 
No immortals are men. 
In the same way, ' All the righteous are happy,' is con- 
verted into ' No unhappy persons are righteous/ 

Hypothetical Inference . 

30. Hypothetical Propositions are of two kinds — Con- 
ditional and Disjunctive. They have been treated as the 
of a distinct form of Syllogism, "called the Hypotheti- 
cal Syllogism, 

If the education of children is neglected, they will grow up 

rant, 1 is regarded as the major premise of a syllogism; 

I by adding, as minor, 'now certain children have been 

glected,' we are entitled to the conclusion, ' they will grow 1 

up ignorant. 1 This has been called a Hypothetical Syllogism 

wditional). ^ By a Disjunctive Proposition (A is either B or 

mpled with a proposition giving one alternative (A is 

m to infer the other alternative (A is C); whieh 

i be a Disjunctive Syllogism. 

In his Lectures on Logic, Sir W. Hamilton, following the usual 

takes up hypothetical reasoning after Syllogism; but in 

at the end, published after his death, he prefers to treat 

it as a case of Immediate Inference. Mr. Mansel, also, argues that 



CONDITIONAL INFERENCE. 117 

hypothetical reasoning, so far as it is purely logical, is purely cate- 
gorical. The obvious differences between the syllogism and hypo- 
thetical reasoning are (1) the absence of a middle term; in tin- 
hypothetical syllogism all the terms are introduced in the so-called 
major; (2) the minor and the conclusion indifferently change 
places, and each of them is merely one of the two members con- 
stituting the major; (3) the major (so-called) consists of two 
propositions, the categorical major of two terms. 

The Conditional form applies in the first instance to cause and 
effect. If the cause is present the effect is, and if the effect is 
absent the cause is absent. But the same form holds good when 
one thing is the sign of another, or is constantly associated with 
that other. 

Book and De Morgan are of opinion that the hypothetical in- 
ference is not different from immediate inference. Boole observes 
in his ' Laws of Thought' (p. 241) that the hypothetical syllogism is 
no syllogism at all, as it need contain no more than two terms. 
De Morgan says — * The law of thought connecting hypothesis 
with necessary consequence is of a character which may claim to 
stand before syllogism, and to be employed in it, rather than the 
converse.' (Syllabus, p. 66). 

31. In tha Conditional Proposition— If A is B, C is D, 
the equivalent is — A being assumed to be B, it follows 
that C is D. 

There is no inference in this case. Accepting * A is B/ we 
accept * C is D ;' this is another expression for the same fact. 
'If the weather continues fine, we shall go to the country', 
is transformable into the equivalent form ' The weather 
continues fine, and so we shall go to the country.' Any 
person affirming the one, does not, in affirming the other, de- 
clare a new fact, but the same fact. No new matter is intro- 
duced into the assertion ; it is a pure instance of the Law of 
Consistency. When a buyer offers a seller a certain price for 
an article, and the seller says, — Here, then, is the article — the 
buyer is only consistent with himself in paying the price. Yet 
this is all that is done in a supposed conditional inference. 

A second form of so-called conditional inference, is that the 
denial of the consequent is the denial of the antecedent; 
I C is not D, therefore A is not B.' If the weather is fine, 
we go to the country ; ' ' we are not going to the country, 
therefore the weather is not fine.' This is still mere formal 
equivalence. It is implied in what has already been stated. 
It is not a distinct fact, but the same fact, in obverse. ■ X is 
followed by Y ' implicates one of two statements ; X has 
happened, hence Y has followed ; or, — Y has not happened, 



118 EQUIVALENT PROPOSITIONAL FORMS. 

not happened (if it did, T would follow). Snch 
.fold hearing of a conditional proposition, 
i down, as part of the theory of Conditional Proposi- 




iot prove ho has caught the infection, because there are 
»f death, besides the one mentioned. This rule, 
or precaution, is therefore grounded on our experience, which 
informs us that in nature there frequently occurs a plurality 
of causes. The case is parallel to the rule for the conversion 
of a Universal Affirmative, which depends on our knowing as 
a fact that iii such affirmations, the predicate is not necessarily 
■ive with the subject, but is most frequently larger 
than the subject. 

li' the condition given were the sole condition of the conse- 
quent, the affirmation of the consequent would be the affirma- 
tion of the antecedent. 'If force is expended, an equivalent 
force will be generated' is a statement containing the one 
indispensable condition of the effect (an equivalent force 
generated). Under all possible circumstances, the production 
of force supposes a prior force expended : hence the affirma- 
tion of the consequent (the generation of force) is the affirma- 
tion of the antecedent (the expenditure of force). Such condi- 
tionals, however, being the exception, and not the rule, logicians 
forbid the affirmation of the antecedent from the affirmation 
of the consequent. 

On the same ground it is forbidden to deny the consequent, 
because the antecedent is denied ; A is not B, therefore C is 
not D ; ' the man has not caught the infection, and therefore 
he will not die.' 

common form of conditional proposition is when both the 
members are affirmative. But either member, or both, maybe 
• ive. There are thus four forms :— 
If A is B, C is D. 

If A is not B, C is D. < If the rebellion be not crushed, the 
will be executed.' It is equally proper to say that the rebel- 
lion having been successful, the king's execution is certain, or that 
it t he king is not executed, the rebellion has been crushed. ' If the 
ronot agree, they will be discharged.' If the jury be not 
urged they have agreed. 'If succour be not speedily sent, 
•y will surrender.' If the city does not surrender, succour 
Bent, 
(jtt If A is B C is not D. ■ If the will of Henry VIII. was 
L - J 1 ** *o legal title to the throne of England : If 
■ I. had a legal title, then the will of Henry was not valid.' 



DISJUNCTIVE INFERENCE. 119 

1 If the harbour is frozen, the ships cannot come in : If the ships 
can come in, the harbour is not frozen.' So ■ He can't be wroM 
whose life ism the right: If he is wrong, his life is not in the riirfat' 

(4) If A is not B, C is not D. « If inspectors be not appointed 
no regard will be paid to the act.' This implies that if the aol la 
observed, inspectors have been appointed. * No Bishop no Kin<* ' 
If the king is, the bishops are. ' If there be no God,' no futuro 
life awaits us : If a future life does await us, there is a God.' 

These forms are all regulated by the same law of transposition 
The chief interest of (2) and (3) lies in this, that when both forms 
apply to two propositions, the union of the two is equivalent, as 
we shall see, to a disjunctive proposition. 

32. The Disjunctive Proposition may appear in the 
following forms : — 

I. A is either B or C. 
II. Either B or C exists. 
III. Either A is B, or C is D. 

4 He is either a fool or a rogue ' means ' If not a fool, he is 
a rogue, and if not a rogue,»he is a fool.' Otherwise, fc Not 
being a fool, he is a rogue/ and 'Not being a rogue, he is a 
fool.' These are all equivalent forms ; and the supposed rea- 
soning consists merely in electing one alternative, according to 
the facts of the case. The datum being, ' he is a not a fool/ 
we use the alternative ' he is a rogue/ and so on. 

This corresponds to the working out of a Logical Division. 
' Feelings are either pleasures, pains, or neutral excitement.' 
The equivalent propositions are such as these : — a feeling not 
a pleasure, is either pain, or a neutral state ; a feeling not a 
pain, and not neutral, is a pleasure ; a feeling not neutral is 
either pleasure or pain, and so forth. There is no real infer- 
ence in these transmutations. They are strict equivalents of 
the original Disjunctive Division. 

Compared with the Conditional propositions, this form 
exhibits a greater degree of complexity in the relation of 
dependence. The Conditional form expresses a simple or 
one-sided dependence ; the presence of the first gives the 
presence of the second, and the absence of the second implies 
the absence of the first. The Disjunctive proposition indicates 
a double or reciprocal dependence ; the presence of either is 
the absence of the other, and the absence of either is the 
presence of the other. This is the ordinary case, but the 
disjunctive form might be employed when the presence of 
either implied the presence of the other, the absence of either, 
the absence of the other. Thus, ' Everything in nature is 



120 EQUIVALENT PROPOSITIONAL FORM& 

r inert or lias no weight.' From this we derive the 

following : — . 

( 1 ) It is inert, and so it has not no-weight = it has weight. 
(■J; It is n->t inert, and so it has no weight. 
(S) It lias no weight, and so it is not inert. 
(-1) It lias not no-weight, i.e. it has weight, and so it is inert, 
ing to the double negation, this form is very awkward ; 
an intermediate stage between the conditional 
, the ordinary disjunctive propositions. 

u must either pay a fine or go to prison* implicates 
four facts : — 

( 1 ) If you pay the fine, you don't go to prison. 

(2) If you don't pay the fine, you go to prison. 

(3) If you go to prison, you don't pay the fine. 
If you don't go to prison, you pay the fine. 

A disjunction is not thoroughgoing and valid unless it gives 
four true propositions in that form, and the only sure test of 
ilidity is to put it through the forms. Thus : — 
4 Either the witness is perjured, or the prisoner is guilty/ 

(1) If the witness is perjured, the prisoner is not guilty. 

(2) If the witness is not perjured, the prisoner is guilty 
(8) If the prisoner is guilty, the witness is not perjured. 
(1) If the prisoner is not guilty, the witness is perjured. 
The propositions (2) and (4) are correct, but (1) and (3) 

could not be maintained. This reveals a weakness in the form 
of the statement. Put thus—* If the witness tells the truth, 
the prisoner is guilty ' — the assertion is perfectly accurate, for 
the witness may be perjured, and still the prisoner may be 
guilty; or the prisoner may be guilty, and still the witness 
may not have told the truth. 

4 Punishment is intended either to repress crime or reform 
riminal.' 

4 If punishment represses crime, it does not reform the crimi- 
nal (1).' Here we see at once that both things may concur. 

'Either the ballot must be given, or intimidation will 
prevail. 1 

W intimidation does not prevail, the ballot exists (4). This 
would not be affirmed, and therefore the disjunction is not 
thoroughgoing.; 



1 Vor many years past, this country has been governed 
either by the Whigs or by the Tories' leaves open a third 
namely, by a coalition. 

4 He either cannot, or will not, do it ' leaves open the supposi- 
tion of 'neither.' 



DILEMMA. 121 

'The substance held in solution is either lime or xnagni 
is an example from chemistry, and deserves to bo pat through 
all the forms, as each form is a test. 

(1) If the reaction of lime is given, magnesia is not pre 

(2) If the reaction of lime is not given, magnesia is present. 

(3) If the reaction of magnesia is given, lime is absent. 

(4) If the reaction of magnesia is not given, lime is present. 
A chemist would not be satisfied without trying two of 

these forms, a positive and a negative. 

33. The Dilemma combines a Conditional and a Dis- 
junctive proposition. 

If the Antecedent of a conditional is made disjunctive, there 
emerges what Whately calls a simple Constructive Dilemma. 
If either A or B is, C is. 
Now, either A or B is. 
Therefore, C is. 
If either plants or animals are found, there must have been 
previous germs. 

Now, either plants or animals are found. 
Whence, there have been previous germs. 
The Consequent being made Disjunctive, gives the more 
usual type : — 

If A is, either B or C is. 
If the barometer falls, there will be either wind or rain. 
Various suppositions may be made, bringing out the possible 
alternatives. Thus — 

A is ; then, B or C is. 

C is not ; then, If A is, B is. 

C is ; then, If A is, B is not. 

B is ; then, if A is, C is not. 

B is not ; then if A is, C is. 

B is not, and C is not ; then, A is not.* 

• Another form of simple Dilemma is 

If B is, A is ; and if C is, A is. 
Now, either B or C is. 
Whence, A is. 
This form is illustrated hy a sentence from Macaulay : — 
Predestination makes men immoral ; for if a man be an heir of grace, 
his exertions must be useless ; if an heir of wrath, they must be unavailing. 
If a man be an heir of grace, his exertions are useless ; if of wrath, 
unavailing. 

But, according to predestination, a man is an heir either of grace or of 
wrath; therefore, according to predestination, his exertions must be 
useless. 

But he who believes his exertions to be useless must be immoral ; 
therefore, predestination makes men immoral. 



11' L> EQUIVALENT PROPOSITION AL FORMS. 

This last is the true dilemma, which is Destructive. The 
re equally valid, and are occasionally appli- 

For instance — 
If the orbit of a comet is diminished, either the comet passes 
thn»,; sting medium, or the law of gravitation is partially 

inspfendi 

But the second alternative is inadmissible. 

ace, if the orbit of a comet is diminished, there is a 
LDg medium. B i ^ 

a conclusion is a simple conditional proposition, the com- 
plexity having been reduced. 

The following are examples of the common Dilemma : — 
If a classical education is worth the cost, either it must be 
pre-eminently fitted to develop the mental powers, or it must ) 
tarnish exceedingly valuable information. Bat neither alter- 
native can be maintained, and so a classical education is not 
worth the cost. 

If schoolmasters can claim exemption from poor's rates, it 
must be either by statute or by the common law. Now, no 
statute exempts them ; and the common law does not apply. 
He nee they can claim no exemption from Poor's Rates. 

Sometimes the antecedent is more conveniently put in the 
form of a question. 

How do we know that our intuitive beliefs concerning the 
world are invariably true ? Either it must be from experience 
establishing the harmony, or an intuitive belief must certify the 
correctness. 

Now, experience cannot warrant such harmony except in so 
is it lias been perceived. Still more futile is it to make one 
instinctive belief the guarantee of another. Thus we cannot 
know that any intuitive belief is universally valid. 

The Dilemma, although occasionally a useful form, is per- 

oftener a snare. The point is whether the disjunction is 

: ; and there is always supposed the rejection of many 

ible eases. We begin with— If A is, B or C or D or E is. 

One after another of the suppositions is rejected, until at last only 

ire left, and these being removed, the antecedent is finally 

1. The illusive case is when the logician trusts to the 

t excluded middle as a guarantee of the disjunction. If 

A is, A is either B or not-B. We may easily afhrm that A is 

I, but how can we affirm that it is not not-B, i.e. it is neither 

anything else than B. It is plain that if we were able 

to affirm that A is not anything else than B, we should not 



EXAMPLES OF THE DILEMMA. 123 

require a dilemma nor yet the term B to disprove A's exist' 

As an example of a false disjunction, we may take the ancient 

fallacy of Motion. 

If a body moves, it must be either in the place where it is, 
or in the place where it is not. 

But a body cannot move in the place where it is, nor yet 
in the place where it is not. Hence, a body cannot move at all. 

The disjunction to conform to the law of Excluded Middle 
must be in this form : — 

The body must move in the place where it is, or it must not 
move in the place where it is. We then admit that a body 
does not move in the place where it is, and the possibility of 
motion is still un destroyed. 

4 If the books in the Alexandrine Library be in conformity 
with the doctrines of the Koran, there is no need of them, if 
they are adverse to the doctrines of the Koran, they should be 
destroyed/ This is not exhaustive, as the books might not 
treat of religion ; but the assertion implies that no knowledge 
is desirable except religious knowledge. 

4 A Berkeleian is reduced, in truth, to this dilemma : if he 
knows what external things are, it can only be by perceiving 
them as external, — which contradicts his theory. If, on the 
other hand, he does not know what they are, he is incapable of 
using the expression external with any meaning, and could, in 
fact, never have invented or thought of employing it.' This 
assumes that the meaning of ' external objects ' is not in dis- 
pute ; it is a summary mode of stating one side ; Berkeley 
could say that the meaning of external objects was just the 
point in dispute. 

Synonymous Propositions, 

34 Every language contains various wordings for the 
same matter of fact ; and there is occasionally an advan- 
tage in passing from one of these to the other. We may 
call these variations Synonymous Propositions. 

There being, in many instances, a plurality of names for 
Che same object, or the same fact, we find them freely inter- 
changed. The essential characteristic of all material substance 
is expressed as Resistance, Force, Momentum, Inertness, all 
which means the same thing, although viewed in different 
aspects. 

4 Men are mortal/ l all will die,' * we are doomed to dissolu- 
tion/ * decay is the law of our being ' — are mere synonymous 



124 EQUIVALENT PROPOSITIONAL FORMS. 

3 that add nothing to the fact, but may contribute to 

ls that down, therefore, it is heavier, is not a 

inference; the two expressions signify one operation. 

-io other criterion of the comparative heaviness of 

: bings, but weighing them. This block of marble is larger 

that, therefore, it is heavier, is a real inference. The 

size is given as the evidence of superiority in another 

and different quality, weight. 

1 What has been, will be ; * ' the future will resemble the 

;' 'nature is uniform;' 'the laws of the universe are 

in t .» — these are all synonymous expressions for the same 

fundamental fact. One of them cannot be tendered as the 

u or evidence of another. The multiplication of forms may 

aid in expounding the great truth underlying them all. One 

form may be suggestive of one class of examples, a different 

form may suggest another class. The variation of language is 

often a great intellectual help. It is, however, a source of 

danger. One of the lures and snares of language lies in the 

tendency of the mind to suppose that two different forms of 

expression mean two different things. Hence, it is a common 

fallacy, and a device of Rhetoric, to give a fact as the reason 

for itself; there being merely a change in the expression. 

There is often a difficulty in finding a single satisfactory ex- 
pression for notions and truths of great generality. Thegreatlaw 
of the Conservation of Force, needs the aid of other terms to 
suggest all its meaning — Persistence, Exchangeability, Equi- 
valence, Correlation. The grounds of the Transcendental 
part of Algebra, called the Differential* Calculus, have been 
viewed in a great variety of aspects, expressed by different 
names — Exhaustions, Limits, Prime and Ultimate Ratios, 
Evanescent Quantities, Fluxions, Differential Co-efficients. 

The elements of the mind called intuitive by the a priori 
school of philosophy, are stated sometimes under the guise of 
the Notion, and sometimes under the guise of the Proposition ; 
the subject matter being identical. We may say either * Cause* 
is an innate notion; or ' every effect must have a cause ' is an 
innate proposition, principle, or judgment. 

The Dictionary mode of defining words consists in giving 
tautologous phrases, which shows that these abound in lan- 
guage. If there were only one name for one thing, an Eng* 
lish Dictionary, conceived on the usual plan, could not exist. 



ASPECTS OF THE PROPOSITION. 125 



EXERCISES ON PROPOSITIONS, INCLUDING NOTIONS. 

The following are examples of Propositions, to be used 
as exercises, in connexion with the Classification of Pro- 
positions, and the Equivalent Forms. As every real pro- 
position has two notions, while even verbal propositions 
contain at least one notion, the examples will also furnish 
exercises on the Notion. 

As regards the Class or Hotion, in opposition to the Real 
Proposition, the points to be illustrated are comparatively few. 
An Individual or Singular object or thing may be exhibited in 
contrast to classes or Generalities ; Homer to poets, the Rhine 
to rivers ; Britain to sovereign states. Of generalized things, 
we have the Class (concrete), and the Attributes (abstract). 
The grades of generality may be exemplified, — a very valuable 
exercise. There remains only the illustration of Relativity, 
the assigning of the correlative class or notion in a definite 
universe. 

The Notion often condenses in a word what would require 
one or more propositions to express in full. Refraction, Elec- 
tricity, Crystallization, Chemical Affinity, — are names for com- 
plex facts, involving many propositions, and not to be explained 
wiihout giving these propositions. * Refraction' is the sum- 
mary designation of the principle or law of the bending of 
light in passing from one transparent medium to another ; and 
its full and proper expression is the law itself given as a real 
predication. 

The various aspects of the Proposition, exhibited in the 
foregoing chapter, may be summarized as follows : — 

I. As Individual or General, and as of different grades of 
Generality, under which is brought out the diminishing Con- 
notation or Comprehension that accompanies increasing Gene- 
rality or Extension. 

The principle of Relativity applied to Propositions, appears 
under various subsequent heads — Negation, Opposition, and 
Ob version. 

II. As possessing Quantity and Quality, with reference to 
the uses of Syllogism. 

III. As Complex in contrast to Simple ; the important 
logical example of Complexity being Hypothetical proposi- 
tions (Conditional and Disjunctive). 

IV. As opposed hi the various modes named Contraries, 
Contradictories, &l*. 



Bfi ON PROPOSITIONS, INCLUDING NOTIONS. 

V M in their final Import, affirming Equality, Co-exist- 

sion ; the two last containing the special kinds 
•tively Co-inhering Attributes and Causation. ^ 
connexion, there might be given the particular 
that the proposition belongs to :— as Mathematics, 
y, Psychology, &o. For although propositions of 
1 1 it v 'make up the one science, Mathematics ; those under 
wo other heads— Co-inhering Attributes and Causation- 
are distributed among several sciences. 

V I As having numerous Equivalent Forms, namely General 
ami Particular, Greater and Less in Connotation, Obverse, 

rem, Hypothetical Equivalents, Synonyms. 

VII. All the foregoing classes suppose real predication. It 

is, however, important to taking every opportunity of contrast- 

Real with Vekbal propositions. A farther interest 

ches to the difference between predicating a Proprium and 

predicating a Concomitant 

Many of the propositions occurring in common speech are 
not certain, but only probable ; the affirmation holds not in all 
3, but in a very great number, as * Temperate persons are 
long lived.' The subject of Probability belongs to the Induc- 
tive Logic, and has not been adverted to in the foregoing 
itication. Still, the distinction of probable and certain is 
so easily understood, in the main circumstance, and so im- 
portant to be born in mind, in matters of truth ^,nd false- 
he od, that it should be impressed on every suitable oppor- 
tunity. 

At the present stage, consideration is given, not to the actual 
truth and falsehood of propositions, but only to what they pro- 
The proof or evidence of assertions belongs to the sub- 
sequent heads — Deduction and Induction. 

Of the following examples, promiscuously chosen, the vari- 
ous forms are to be used according to their peculiar suitability 
I lie different classes of propositions. In a large proportion 
Of them, there is scope for translating the idioms of ordinary 
language into modes of expression more in accordance with 
the logical forms. 

: Honesty is the best policy.' 

A proposition of a certain grade of Generality ; one relating 
to 'virtue ' would be more general ; one relating to * paying 
one's debts ' would be less general, but would have a more 
comprehensive predicate. 

As regards Quantity and Quality (in Form), it is a universal 



EXAMPLES OF PROPOSITIONS. 127 

iffirmatiye; being translateable into ' all honest actions aro 
nore politic than actions not honest.' 

We read, in Otway, ' Honesty is a damned starving quality,' 
vhich is the full Contrary. The Contradictory is, 'Some 
lonest actions are not good policy.' 

In Import, the proposition is one of Causation—' Honest 
ictijus bring good consequences to the agent.' The subject 
aeing Mind, it belongs to the science of Psychology. 

Many Equivalent Forms could be given — « Some honest 
ictions are politic.' Obversion (Formal): — • Honesty iW not 
oad policy;' 'No honest men are unsuccessful men ;' (Material) 
■ Dishonesty is bad policy.' Conversion : — • Some politic 
ictions are honest actions/ 

The proposition is not verbal but Real ; good policy is not, 
in whole or in part, the definition of honesty. It is a Pro- 
prium, or derivative proposition, and not an ultimate fact ; it 
is deducible from the operation of honesty, under general laws 
of cause and effect in the human mind. 

It is a proposition, not certain, but Probable. It is true, not 
nniversally, but in a large and preponderating number of 
cases. 

'All the alkalies and alkaline earths are oxides of the 
metals.' A complex affirmation, containing two in one, which 
must be taken separately. In form and import, they are so 
closely allied, that one may represent both. 

As regards External Form, each is an example of A, with no 
peculiarities requiring attention. 

In Import, they belong to the class of affirmations of Co- 
inhering Attributes, and fall under Chemistry. 

Strictly analyzed, each is a verbal proposition; the predicate — 
oxides of the metals —is now given as one of the essential 
characters of Alkalies, and of Alkaline Earths. In the origi- 
nal connotation of these words, however, the composition or 
derivation of the substances was not taken into account ; the 
main fact was the relation to acids, and to neutral salts. At 
that stage, Davy's discovery was an additional fact, and there- 
fore a real predication. In so far as the terms still suggest 
to the mind only the primitive meaning of an Alkali, the 
proposition is but real, not essential and verbal. 

' Fishes breathe by gills.' Equivalent to 'All fishes.' A 
verbal or essential proposition of Kinds ; the subject ' fishes' 
connotes all the essential attributes of fishes, of which the pre- 



128 EXERCISES ON PROPOSITIONS, INCLUDING NOTIONS. 

As the structure is confined to fishes, the subject 
BIll i b co-extensive. It is a proposition in Biology, 

id to health is exercise.' An inversion for — ' Exercise 
tea health.' 'All persons that take exercise use 
s to health.' A proposition of Cause and Effect, 
! liologj. A Ileal proposition. 

in is a consequence of Sensibility.' (Concrete) All 

sitive being are beings subject to pain; all sensitive beings, 

under curtain circumstances, are pained beings. A Verbal or 

analytical proposition ; ' being subject to pleasure, to pain and 

neutral excitement/ is the definition of/ Sensitive.' Might 

riven to illustrate the Aristotelian distinction of the Poten» 

and the Actual. 

' Whatever is, is right.' The generality of the subject is even 
beyond the two summa genera — Object and Subject. Exist- 
ence is a fictitious predicate, and, in intelligible propositions, 
means something more definite than it seems. The proposi- 
tion must be interpreted — ' all the arrangements of the world 
right, or are good.' In Import, this is Cause and Effect. 
The obverse is * nothing that is, is wrong/ * there is no wrong.' 

* The Beautiful and the Useful are partially coincident ; ' a 
synonymous form for — Some Beautiful things are useful, and 
conversely. 

'The wages of sin is death,' or Death is the wages of sin. 
This form would suggest a universal co-existence between 
Death and Sin — all beings that die are all beings that sin. 
Another interpretation is 'Adam's sin was the cause of 

death.' 

1 Self-confidence is not inconsistent with great weakness.' 
-confident persons may be weak persons.' This is a con- 
tradictory to 'All self-confident persons are strong.' 

Ot a similar nature is — ' A proud man is not necessarily a 

bad man.' 

ii is the only animal combining sociability and solitude. 
A form equivalent to the universal Quantification of the Predi- 



EXAMPLES OF PROPOSITIONS. 129 

cate, and useful to test De Morgan's criticism as to the denial 
of such propositions. 

Take together the 47th and the 48th propositions of tho 
First Book of Euclid, and show their bearing on universal 
quantification. 

' Adverbs qualify verbs ; * ' Adverbs are to be placed near 
the words they qualify/ How do these differ logically ? 

4 The greater the novelty, the greater the pleasure/ A 
proprium or inference from ' Novelty is a source of pleasure.' 
In propositions of cause and effect, we are entitled to infer 
the proportionality of the one to the other. 

* Symmetry is the general law of creation ; ' a greatly distorted 
expression of what is meant. ' Symmetry ' is a word condens- 
ing a proposition ; and the sounding phrase * the general law 
of creation ' signifies merely that a fact is frequent or usual. 
'Many (or some) things in nature are symmetrically con- 
structed.' 

The angle in a semicircle is a right angle. 
Ice is cold. 

The diamond is surpassingly brilliant. 
Extreme heat destroys life. 
Motion follows the line of least resistance. 
Truth is more easily extricated from error than from con- 
fusion. 

An age of ignorance is an age of ceremony. 

Power corrupts the mind. 

Time abates grief. 

Custom blunts sensibility. 

Private vices are public benefits. 

Uneasy lies the head that wears a crown. 

Tyranny is irresponsible power. 

Benevolence is the sum of virtue. 

Distance lends enchantment to the view. 

Consumption is a fatal disease in this country. 

International law has no written statutes. 

Conception is involved in every act of perception. 

None but the brave deserve the fair. 

Not being rich is not always an evil. 

All is not gold that glitters. 



130 EXERCISES ON PROPOSITIONS, INCLUDING NOTIONS. 

The causes of strength are not pledges for its continu- 

every advice is a safe one. 

,1 need not be attempted. 

lool. 

i^ood news. 
men are placed in exalted situations and free from envi- 

od orators are not always good statesmen. 
There are studies much vaunted, and yet of little utility. 
Few even of our best aspirations are gratified. 
Hardly any virtue is quite safe from passing into a vice. 

The two following extracts are from Plato — 
4 All men who have gout, or fever, or ophthalmia, are sick; 
but all sick men have not gout, or fever, or ophthalmia. So, 
11 carpenters, or shoemakers, or sculptors, are craftsmen ; 
but all craftsmen are not carpenters, or shoemakers, or sculp- 
In like manner, all madmen are unwise ; but all unwise 
men are not mad. 

1 Whosoever is a good rhapsode, is also a good general ? 

iestionably. And, of course, whoever is a good general, 

is also a good rhapsode ? No ; I do not think that.' 

* The objects bring up the feelings, and, conversely, the feel- 
t he objects.' In this sentence, is the word 'conversely* 
used in its proper meaning ? 

If steam is passed over red hot iron, hydrogen will be 
evolved. 

\( virtue is knowledge, it is teachable. 

It the footmarks were made by. the prisoner, he must have 
worn shoes too small for his feet. But he could not have 
done so. What then ? 

H the soul is incorruptible, it is ingenerable. 

.Matter is either solid, or liquid, or gaseous. 

Mr. de Morgan supposes a stump orator intending to say— 

aU Englishmen are lovers of liberty; and declaiming in these 

J8 :- bhew me any number of men, and I will say with 

lence either that they will with one accord raise their 

* Dices for liberty, or that there are aliens among them.' This 

might be regarded as an equivalent statement, without syllo- 

to inference. ' J 

Cromwell, on his death-bed, is said to have asked a divine 



EXAMPLES OF PROPOSITIONS. 131 

who was with him, whether it was possible to fall away from 
grace. The answer was, — It is not possible. Then, 
Cromwell, I am safe, for I was in grace once. 

No form of polity is so admirable as a limited constitutional 
monarchy ; for it is, beyond all question, superior to every other 
species of government. 

Honesty is deserving of reward. A negro is a fellow 
creature. An honest negro is a fellow-creature deserving 
reward. 

Every man is an animal. Every head of a man is the head 
of an animal. De Morgan. 

In Book IY — The Logic of the Sciences — as well as through- 
out the work generally, there occur numerous examples that 
may serve as additional exercises if necessary. 









, 



BOOK II. 

DEDUCTION. 



CHAPTER L 

THE SYLLOGISM. 

1. The Syllogism is the fully expressed form of a De- 
ductive Inference, that is, an inference from the General to 
the Particular. 

When a step of reasoning or argumentation consists in as- 
signing, as the proof of an affirmation (or denial), some more 
general affirmation, it admits of being stated in a peculiar 
form, in which there is sometimes greater facility in judging 
of its soundness. The peculiarity of the form of statement 
consists mainly in this, that everything belonging to the rea- 
soning is set forth explicitly. Thus, when any one maintains 
that Mathematics is useful as a mental discipline, and assigns 
as the proof, that all the exact sciences are useful as mental 
discipline, the reasoning, which is Deductive, and not Induc- 
tive, contains these two assertions : — (1) All the exact sciences 
are useful as mental discipline ; (2) Mathematics is an exact 
science. Both these are indispensable to the conclusion 

* Mathematics is a mental discipline.' The first is the general 
principle, the second an intermediate proposition for applying 
the general principle to the case in hand. Very often, one of 
the two propositions is left unexpressed. In the example : 

* this man is a rogue, therefore he is not to be trusted,' there 
is an ellipsis of the general principle — ' rogues are not to be 
trusted.' In the form 'you cannot trust rogues, therefore you 
cannot trust this man,' the omission is in the second or apply- 
ing proposition — ' this man i* a rogue.' 



13-1 THE SYLLOGISM. 






A Deductive reasoning fully and formally expressed is a 
Syllogism. 

16 following arrangement — * 

(1) All men are fallible, 

(2) John is a man, 

(3) John is fallible— 

is a regular ded active reasoning, or an argumentation in the 

o or complete form. The two first propositions 

combine to make the proof of the third ; they are called the 

of the reasoning or syllogism ; the third is the point 

to be proved, and is called the Conclusion. 

We shall see hereafter that, in the departures made from the 
regular form of the syllogism, the order of the propositions 
may be reversed ; the applying proposition coming first, and the 
grounding proposition second. But whatever form the syllo- 
gism may assume, one feature can never be absent — a general 
proposition. This is indispensable. Unless one of the premises 
be more general than the conclusion, the argument is not 
deductive. 

2. A Syllogism is said to contain three, and only three 
Terms ; the Subject and the Predicate of the Conclusion, 
and another Term, occurring in both Premises ; the Sub- 
ject of the Conclusion is the Minor Term ; the Predicate 
of the Conclusion, the Major Term ; the term occurring in 
both Premises, is the Middle Term. 

By ' Terms • are meant the expressed notions entering into 
the subjects and predicates of the propositions. A proposition 
couples or unites two Terms. * X is Y ' contains the two terms 
X and Y affirmatively conjoined. * Men are not gods ' contains 
the two terms ' men ' and ' gods ' under a negative copula. 

In seeking out the Terms, we begin with the proposition to 
be proved, that is, the conclusion. The subject of the conclusion 
is the Minor or smaller term, the predicate the Major or greater 
term. The propriety of these designations is grounded on 
the circumstance, formerly adverted to, that in propositions 
generally, the predicate covers the subject, and other subjects 
les ; ' kings are fallible,' and many other beings besides 
kings are fallible ; hence 'kings ' are a smaller group forming 
of a larger group ' fallible ;' in compass or extent, there- 
toie, * kings ' are a Minor term, ' fallible ' a Major term:* 

: W Hamilton complains that these designations are false and 
DQfl because they do not apply to the terms "as considered in Com- 
osion. fhere ait, more men than kings, and so the designations are 



ZZirO 



TTIE THREE TERMSJ^ 135 



The Middle Term must be sought not in the conclusion, bnfc 
n the Premises, or proving propositions, and must appear in 
)oth. Thus, in the syllogism — 

Men are fallible, 
Kings are men, 
Kings are fallible. 
The term, absent from the conclusion, and present in both 
>remises, is ' men/ the subject of the first and the predicate of 
,he second. It is called ' middle ' because it is the medium or 
nstrumentality for bringing together in the conclusion, the 
najor and minor terms ; they being separated in the premises. 
<Uso, as regards extent, compass, or denotation, it is inter- 
nediate thus : — The minor ' kings' is less in extent than 6 men ;' 
nen are more numerous than kings. Again, * men ' is less in 
jxtent than ' fallible beings ; ' there being many fallible beings 
jesides men. So ' men ' being more extensive than the minor 
ierm * kings/ and less extensive than the major term ' fallible 
jeings,' is properly a middle or intermediate term. The grada- 
;ion is represented in a diagram thus : — 

Fallible, • . . major, 

Men, . . • • middle, 

Kings, . . minor. 

Although the syllogism contains three propositions, each 
svith two terms, making six terms in all; yet, in virtue of 
:he double occurence of each? there are in reality only three 
:erms. The example shows : — 
The Middle term in both premises. 
The Minor term in the conclusion and in one premise. 
The Major term in the conclusion and in one premise. 

3. In the Syllogism, there are Three, and only three, 
Propositions, namely, the two Premises and the Conclusion. 
The Premise containing the Major Term and the Middle 
Term, is called the Major Premise ; the Premise contain- 
ing the Middle Term and the Minor Term, is called the 
Minor Premise. 

In the foregoing example, the Premise first in order contains 

ipplicable to the extension of the terms ; but, he argues, more attributes 
ire connoted by the term ' kings' than by the term men, and so major 
md minor are inapplicable to the comprehension. In criticism of this 
view, it may be said that confessedly the designations major and minor 
are applicable to the terms viewed in their compass or extension, that these 
terms are used in that sense, that they cannot be used without confusion 
in both senses, and that Hamilton has shown no good reason for invert- 
ing the common usage. 



^gg THE SYLLOGISM. 

the Major term 'fallible,' together with the Middle term, 

'men are fallible;' this is the Maj or Premise. Ihe 

Premise second in order contains the Middle term, 'men and 

Minor term, ' kings/- 4 kings are men —and is the Minor 

find it convenient to represent the forms of the syllogism 
by Letters or symbols, thus :— Let X be the minor term, Y, the 
middle term, Z, the major term ; then- 
All Y is Z 
All X is Y 
AllXisZ 
is a syllogistic form on the basis of affirmation ; that is to say, 
the universal proposition in the first premise is affirmative, and 
the conclusion is affirmative. 

An example on the basis of negation is — 
No Y is Z 
All X is Y 
No X is Z, 
or, by Hamilton's still more expressive symbols,-— 
S (subject of conclusion, minor term), 
M (middle term), 
P (predicate of conclusion, major term) ; 

All M is P No M is P 

All S is M All S is M 

A11S is P . No Sis P. 

4. Syllogisms, or Syllogistic forms, are divided into 
Figures, according to the position of the Middle Term. 
There are, in all, Four Figures. ] 

The First Figure is exemplified in the forms hitherto em- 
ployed. In it, the Middle Term is Subject in the Major Pre- 
mise, Predicate in the Minor Premise. 

YisZ MisP M — 
X is T S is M — M 
X is Z S is P 
The idea implied under 'Figure' is borrowed from the 
Figures of Rhetoric, which are departures, for effect, from the 
plain and ordinary forms of speech. On this analogy, 
ver, as remarked by Hamilton, there ought to be some 
one regular or standard form, from which all other forms are 
deviations or departures, thence properly called 'Figures.' 
Such standard form is what is mis-named the 'First Figure,' 
which is the pure type of a deductive argument. The Major 
or First Premise is the universal proposition indispensable in 



. THE FIGURES. 137 

deduction, the Minor or Second Premise is an affirmative pro- 
position, whatever may be its quantity. As to order, the Uni- 
versal is placed first, as being of the two premises the funda- 
mental or chief; the nso of the second premise, the minor, 
being to apply the tirst to a particular ease. ' All thieves are 
deserving of punishment,' is applied to a particular instance, 
by means of an affirmation bringing the instance within the 
sweep of the rule, that is, declaring such a one to be a thief. 
This is the function of the minor. 

In the Second Figure, or the first departure from the normal 
syllogism, the middle term is predicate in both premises 
Z is Y P is M — M 
X is Y S is M — M 

Here there is an obvious inversion of the natural order of 
things. In the major premise, Z is Y, P is M, the largest term 
is made the subject, and the middle term the predicate, of the 
proposition. If the proposition be affirmative, this change is not 
compatible with universality, and therefore the proposition can- 
not be the major in the same sense as in the standard syllogism. 
If the proposition be negative, there is only a harmless con- 
version ; we may, for * no Y is Z,' substitute ' no Z is Y ;' * no 
men are gods/ * no gods are men.' This is an insignificant 
and, for the most part, useless alteration of the negative form 
of the standard syllogism. Two of the four forms of the 
Figure (called Moods) are fashioned out of this trivial altera- 
tion. The two other forms containing affirmative majors in- 
volve still greater changes of the standard form. In one, the 
major is not the universal proposition required as the basis of 
the deduction, but the applying proposition, which in the first 
figure is the second or minor premise. In the concluding 
form, there is a much greater distortion, consequent on present- 
ing the normal premises in obverted forms. 

In the Third Figure, the middle term is subject in both 
premises. 

Y is Z M is P M— 

Y is X M is S M— 

Here the major stands as in the first, or normal figure. The 
minor has its terms transposed ; the middle term is subject, 
and the minor term predicate. As before, this is a harmless 
change, if the proposition be a universal negative ; in which case, 
however, the minor premise must be the universal or ground- 
ing proposition, and not the applying proposition ; so that, as 
compared with the standard form, there is an inversion of the 
order of the premises. If the minor be affirmative, either it 



138 the syllogism. 

be particular, or there is some distortion, rendering the 
B different in fact from what they are in appearance. 
In the Fourth figure, the position of the middle term is the 
c reversed ; it is predicate in major, and subject in 

minor. 

Z is Y P is M — M 
Y is X M is S M — 
This double inversion of the order of the terms implies still 
fcer deviations from the primary form. The inversion is 
ible by such devices as above described for the smaller 
inversions in the second and third figures. 

5. Each Figure has a certain number of distinct forms, 
called the Moods, or modes of the figure. The variation of 
mood is determined by the variety of the propositions con- 
tained, as regards Quantity, and Quality. 

The order of the terms is fixed for each Figure ; but the 
propositions constituting the premises and the conclusion may, 
within certain limits, be of one or other of the four forms, 
A, I, E, 0. 

The First Figure, the normal syllogism, has Four Moods. 
The First Mood is composed of three universal affirmations. 
All Y is Z | A, A, A All men are fallible. 

All X is Y > {Barbara) All kings are men. 
All X is Z J All kings are fallible. 

In the Second Mood, 

The Major is a universal negative — E. 

The Minor a universal affirmative — A. 

The Conclusion a universal negative — E. 
No Y is Z 1 E, A, E No men are gods. 
All X is Y \ (Celarent) All kings are men. 
No X is Z J No kings are gods. 

The Third Mood is the first, with a particular minor, and 
particular conclusion ; — 

All Y is Z } A, I, I All men are fallible. 

Some X is Y V (Darii) Some beings are men. 

Some X is Z ) Some beings are fallible. 

The Fourth Mood is a similar variation on the second; par- 
ticular minor and particular conclusion • 

Y t Z ^ ) E .I.O No men are gods. 
Some X is Y £ (Ferio) Some beings are men. 
Some X is not Z ) Some beings are not gods, 

I 



FIRST FIGURE. 139 

These four moods are obviously reducible to two; the third 
and fourth being mere unessential varieties of the first and 
second. The two comprehensive forms may be stated thus : — 
All Y is Z No Y is Z 

All or some X is Y All or some X is Y 
All or some X is Z f No X is Z. 

( Some X is not Z. 

The first form is the normal type of all deduction for an 
affirmative conclusion ; the second, the type for a negative 
conclusion. They present the deductive process in its regular 
order : — 

First, a universal proposition, as the ground proposition of 
the reasoning (Major premise) ; 

Secondly, an affirmative and applying proposition (Minor 
premise) ; 

Lastly, the universal truth applied to the particular case 
(the Conclusion J. 

We desire to prove that kings are fallible, by applying to them 
the principle of the fallibility of all men. The major states 
the principle, the minor applies it. And so for a negative con- 
clusion. 

There cannot be any valid deduction whatsoever but must 
conform to the foregoing type ; whatever variation may be 
made, this is at the bottom. 

The Second Figure has likewise four Moods. 
In the First Mood, 

The Major is a universal negative — E. 

The Minor a universal affirmative — A. 

The Conclusion a universal negative — E. 

No Z is Y } E, A, E, No gods are men. 

All X is Y > ( Cesar e) All kings are men. 

No X is Z ) • No kings are gods. 

This is a case where advantage is taken of the simple con- 
7ersion of the universal negative to make a trivial departure 
Tom the standard (negative) syllogism. Only a slight change 
s necessary to reconvert the present mood to the second mood 
jf the First Figure ; for ' No Y is Z ' 4 No men are gods/ we are 
it liberty to substitute 4 No Z is Y,' 'No gods are men/ which 
.s the whole difference. 

In the Second Mood, 

The Major is a universal affirmative — A, 
The Minor a universal negative — E, 



140 THE SYLLOGISM. 

Tlie conclusion a universal negative — B. 
All Z is Y ) A, E, E, All kings are men. 
r > (Camestres) No gods are men. 
Z j No gods are kings. 

A much greater variation from the standard (negative) is 
re. The grounding proposition, which must be 
universal, is the minor premise : so that there is an inversion 
of the normal order of the premises. Moreover, the same pro- 
»n has been converted simply, from the form ' No men 
_ ;-"ds ;' and the conclusion is likewise the converse of the 
asion in the regular syllogism. By first restoring the order 
of the premises, and next re-converting two universal negations, 
we have the normal negative syllogism (Celarent). 
No men are gods. 
All kings are men. 
No kings are gods. 
The grounding universal is the negative proposition, l no 
men are gods ' — the applying proposition is ' all kings are men/ 

In the Third Mood, 

The Major is a universal negative — E, 
The Minor a particular affirmative — I, 

The Conclusion a particular negative — O. 
No Z is Y J E, I, No gods are men. 
Some X is Y > (Festino) Some beings are men. 
Some X is notZ ) Some beings are not gods. 

Here we remark the same trivial departure from one of the 
standard forms, as in the first mood. The universal negative— 
the major in the fourth mood of the first figure (Ferio)— is 
simply converted (No Y is Z, into No Z is Y ; no men are 
gods, into no gods are men). 

In the Fourth and last Mood, there is a more serious dis- 

tortion. 

The Major is a universal affirmative— A, 
The Minor a particular negative — O, 

The Conclusion a particular negative — O, 

AH Z is Y | A, 0, All gods are men. 

b me X is not Y > {Baroko) Some beings are not men. 

borne X is not Z I Some beings are not gods. 

-lance at the premises shows us that they are not at 

m what they appear on the surface. There is indeed a 

universal proposition in the major premise, which might 

r for the ground proposition ; but then the other pre- 



SECOND F1GUKE. 141 

arise, in that case the applying proposition, is negative, which 
is not allowable. The real fact is that the affirmative major, 
is a negative (universal) in disguise, and the negative minor, 
is an affirmative in disguise. The disguises may bo laid upon, 
thus — 

All Z is Y No not-Y is Z 

Some X is not Y Some X is not-Y 
Some X is not Z Some X is not Z 
The true middle term instead of being Y, is the negative of 
Y, or not-Y (U— Y) This is the key to the distortion. The 
remedy consists in (1) obverting and converting the major — All 
Z is Y, which becomes No not-Y is Z ; and (2) in obverting 
the minor — Some X is not Y, Some X is not-Y. There thus 
emerges a form of the third mood of the first figure (Ferio), 
with not-Y, as the middle term. 

This mood cannot be reduced to a mood of the First Figure 
without Obversion. The older logicians sought to establish its 
validity by a cumbrous process technically known as Eeductio 
ad impossibile. They showed that the conclusion cannot be 
supposed false, without leading to a contradiction of one of 
the premises, which are given as unimpeachable. Thus : — 

All Z is Y 

Some X is not Y 

Some X is not Z 
If c Some X is not Z ' be declared false, the universal ' All X 
is Z,' — which is its contradictory, — must be admitted as trae. 
Taking this new proposition, c All X is Z ' along with the major 
of the original syllogism, 'All Z is Y,' we reach the conclusion 
that ' All X is Y.' Thus :— 

All Z is Y 

AUXisZ 

All X is Y 
is a syllogism in Barbara, But we know from the original 
premises that ' Some X is not Y f it cannot therefore be true 
that c All X is Y.' One of the premises of the above Barbara 
must be unsound. The major 'All Z is Y,' is one of the origi- 
nal premises, granted as true ; the error must lie on the minor, 
4 All X is Z.' Now this is the proposition taken on trial ; and 
its truth being shown to be incompatible with the truth of the 
original premises, its contradictory, ' Some X is not Z ' must 
be true. And ' Some X is not Z ' is the conclusion in question j 
which is thus shown to be valid. 

The Third Figure has six Moods. 



142 THE SYLLOGISM. 

In the First Mood, : • ■ l£ « . 

The Major is a universal affirmative— A, 
The Minor a universal affirmative — A. 

The Conclusion a particular affirmative— I. 
All Y is Z ) A, A, I All men are fallible. 
All Y is X UJJaraptl) All men are living beings. 
Some X is Z ) Some living beings are fallible. 

The only departure, in this instance, from the standard 
syllogism (with a particular minor, Darii) is the universality 
of the minor, All Y is X By simple conversion, this premise 
Uremics Some X is Y, and the syllogism is then the same as 
the third mood of the regular syllogism. 

This figure is quoted as a useful form. Certain reason- 
are considered to fall more readily into the above ar- 
nient, than into the corresponding mood of the First 
Figure. 

The Second Mood contains an inversion of tlie order of the 
Premises. This distortion is altogether gratuitous ; it serves 
no purpose but to seem a variety. 

borne Y is Z^ I, A, I Some men are kings. 

All Y is X y(Disamis) All men are fallible beings. 

Some X is Z ) Some fallible beings are kings. 

Here, if we redress the order of the premises, and simply 
convert the new minor — Some Y is Z, into Some Z is Y, — 
there arises a regular affirmative syllogism, with a particular 
minor (Darii) ; there being only the speciality that the minor 
and the major terms have changed places, thus .— 
All Y is X All men are fallible beings. 
Some Z is Y Some kings are men. 

From this the conclusion would be 'Some Z is X,' 'some 
kings are fallible beings,' which, however, by simple con- 
version, gives ■ Some X is Z,' 'some fallible beings are men.' 

The Third Mood is one of the trival variations of syllogistic 
form. 

All Y is Z ^ A, I, I, All men are fallible. 

ie Y is X WjJo/m), Some men are kings. 
Some X is Z ) Some kings are fallible beings. 

There is no departure here, from the regular syllogism 
[affirmative, with particular minor Darii), but in the minor 
premise, which is Some Y is X, instead of its equivalent, Some 



TIIIKD FIGURE. 143 

The Fourth Mood is exactly the counterpart of the previous 
nood, with a negative major. 

No Y is Z \ E, A, O No men are gods. 

All Y is X > (Felapton) All men are living beings. 

Some X isnotZ j Some living beings are not gods. 

This differs from the negative mood of the first figure/ with 
i particular minor (Ferzo), only in having a universal minor, 
,vhich, by conversion, becomes particular, Some X is Y ; the 
syllogism is then exactly the fourth mood of the standard 
syllogism. 

The Fifth Mood is, in point of distortion, the parallel of the 
last mood of the Second Figure (Baroko). Both the premises 
appear different from what they are in reality. 
Some Y is not Z 1 O, A, O, Some men are not kings. 
All Y is X UBohardo) All men are fallible. 

Some X is not Z ) Some fallible beings are not king's. 

If we look for a universal premise, to supply the ground 
proposition, we seem to find it in the minor; but then the 
other premise is negative, and therefore is not the applying 
proposition. As in Barolco, we must transfigure both pre- 
mises. The present major is made affirmative, by obversion, — 
' Some Y is not-Z,' and is then converted, ' Some not-Z is Y.' 
This is taken as the minor premise, the other being the major, 
thus : — 

All Y is X All men are fallible. 

Some not-Z is Y Some not-kings are men. 
which are the premises of the regular syllogism (affirmative, 
with particular minor, Darii) and would give as a conclusion, 

Some not-Z is X, Some not-kings are fallible, 
or, by conversion and obversion, 

Some X is not Z, Some fallible beings are kings. 

As in the case of Barolco, the older logicians could not refer 
this mood to the First Figure, and applied as a test of its validity 
the Beductio ad impossibile. The process need not be repeated 
at length. We assume the universal contrary to the conclu- 
sion, and taking it along with the given minor, evolve a pro- 
position that contradicts the given major : and argue, as under 
Barolw, that the universal contrary of the conclusion must be 
False, and therefore the conclusion itself valid. 

The Sixth and last Mood is the negative counterpart of the 
third, and should have been placed after the fourth ; it is an 
equally trivial departure from the regular syllogism (negative, 
with particular premise, Ferio). 



144 THE SYLLOGISM. 



No Y is Z ) E, I, 0, No men are gods. 

y (Ferison) Some men are living beings. 
,i >t Z ) Some living beings^are not gods. 

simple conversion of the minor ' Some Y is X,' into ' Some 
living beings are men/ — reproduces Ferlo, in the 
Standard figure. 

The Fouirrn Figure has five Moods. In tbis figure, there is 
nn inversion of both premises as compared with the regular 
Byllogism. Tliis, of course, produces apparently a great degree 
of distortion ; but there is very little in reality. In three of 
the moods, the inversion is caused by the transposition of the 
premises ; this rectified, they need only the simple conversion 
of cue or more of the propositions tq make them standard 
syllogisms. 

Thus, to take the First Mood, which has universal affirmative 
premises, and particular conclusion : — 

All Z is Y ) A, A, I All kings are men. 

All Y is X > (Bramantip) All men are fallible. 

me X is Z J Some fallible beings are kings. 

Transpose the premises, and there emerges a standard syllo- 
gism (affirmative, with universal minor, Barbara)— 
All Y is X All men are fallible. 

All Z is Y All kings are men. 

The conclusion from these premises is — 

All Z is X All kings are fallible. 

This conclusion, converted by limitation, gives — 

Some X is Z Some fallible beings are kings. 

The Second Mood is, if possible, still closer to a regular 
syllogism, when the order of the premises is changed. 
All Z is Y } A, E, E, All kings are men. 
No Y is X V (Camenes) No men are gods. 
No X is Z ) 2STo gods are kings. 

Restore the order of the Premises : — 

No Y is X No men are gods. 

All Z is Y All kings are men. 

These are the premises of the regular syllogism (negative, with 

universal minor, Celarent), and the conclusion is 

No Z is X No kings are gods. 

^Yhence No X is Z No gods are kings. 

The Third Mood is constructed on a similar plan ; the devia- 
from regularity being caused by transposed premises :— 



FOURTH FIGURE. |4J| 

Some Z is Y ^ I, A, I Some living beings are men. 

All Y is X y(Dimaris) All men are fallible. 

Some X is Z ) Some fallible objects are living beings 

With re-transposed premises, — 

All Y is X All men are fallible. 

Some Z is Y Some living beings are men. 

Whence by Darii, in the standard Figure, the conclusion is 

Some Z is X Some living beings are fallible. 

Or Some X is Z Some fallible objects are livin^ beings. 

The fourth and fifth Moods attain their peculiar form not 
through the inverted order, but through the conversion, of the 
Premises. The Fourth runs thus : — 
No Z is Y 1 E, A, No gods are men. 

All Y is X >- (Fesapo) All men are living beings. 

Some X is not Z ) Some living beings are not gods. 

Convert both premises, the major simply, the minor by limita- 
tion : — 

No Y is Z No men are gods. 

Some X is Y Some living beings are men. 
These are the premises of the negative form in the first figure, 
with particular minor (Ferio), whence 

Some X is not Z Some living beings are not gods. 

The Fifth and last Mood differs from the fourth only in 
having a particular minor ; the universality of the minor in 
the fourth being superfluous, as leading to no stronger conclu- 
sion than the present form. The process of assimilation to 
Ferio is precisely the same — 
No Z is Y "J E, I, O, No gods are men. 

Some Y is X > (Fresison) Some men are living beings. 

Some X is not Z J Some living beings are not godg. 

Convert both premises simply : — 

No Y is Z No men are gods. 

Some X is Y Some living beings are men. 

The premises are now in Ferio y whence, 

Some X is not Z Some living beings are not gods. 

The modes of the Fourth Figure, are thus, with the appear- 
ance of great inversion, mere varieties of the primary Figure. 
The transposition of the order of the premises is the most 
insignificant of all the alterations made on a syllogism. It 
signifies nothing to the reasoning, in what order the premises 
are stated. The three first moods depart from the standard 
moods in very little besides. The two last moods, as has 



I^q THE SYLLOGISM. 

en, present both premises converted; and the first of 
pel ilaous, even as a form. 

The prime importance of the Syllogism attaches to its 
adard forms, that is, to the First Figure. In it we learn 
the essential structure of each valid deduction— a universal 
rand proposition, affirmative or negative, and an applying 
position, which must be affirmative. These appear, in the 
adard syllogism, in the order stated— first, the ground 
proposition (the major premise), secondly, the applying propo- 
sition (the minor premise). In the subsequent figures, these 
sometimes transposed; and, in two forms, Baroko and 
, they are greatly disguised. The ground proposition 
nilled by Hamilton the sumption, the applying proposition, 

:ul>fH))il>liou (more strictly, the subsumijig proposition). 
It is not easy at first sight to point out any of the forms of 
the 2nd, 3i*d, or 4th Figures that are of special importance in 
the conduct of reasoning or argumentation. The Fourth Figure 
is the least important of all ; next, perhaps, the second, which, 
with the exception of Baroko, scarcely disguises the standard 
forms. The Third Figure is useful in overthrowing universal 
oppositions, by exceptions or contradictory particulars. 

It was pointed out by Aristotle, that in the First Figure only 
have we conclusions in all the forms, A, E, I, 0. The Second 
Figure is restricted to negative conclusions ; the Third Figure, 
to particulars, The Fourth Figure, which Aristotle did not re- 
j nize, does not admit of a universally affirmative conclusion. 
In explanation of the possible uses of the Figures after the 
first, two circumstances may be remarked that lead to depart- 
ures from the typical form. In the first place, the order of 
subject and predicate in either premise, and consequently the 
figure wherein the syllogism naturally falls, may vary with the 
idea uppermost in the mind of the reasoner. " The best form of 
rernment is Government by a plurality of persons/' and 
-vernment by a plurality of persons is the best form of 
vernment," are variations of the same statement that would 
Be a variation of Figure. In the second place, the extent 
he middle term relatively to the extent of the major and 
miner, gives rise to variations. When the middle term is larger 
than eitner major or minor, it naturally forms the predicate 
b of the major and of the minor premise, producing a syllo- 
m of the Second Figure. When, again, the middle term is 
smaller than either, it naturally forms the subject of both pre- 
mists, producing a syllogism of the Third Figure. 



THE MNEMONIC LINES. 117 

It has been shown in the detailed explanation above given, 
that the fifteen moods of the three last Figures are Btriot 
equivalents of the Moods of the First Figure, and therefore 
have the same validity as these standard moods. The demon- 
stration of this equivalence is technically called the ReduOTIOH 
of the syllogisms, or their revocation to the primitive forms of 
affirmative and negative predication. The necessity offtedno- 
tion depends upon the nature of the proximate canons adopted 
for the syllogism. If those canons are applicable only to 
the First Figure, then, before we can test the validity of 
irregular moods, we must reduce them to moods of the First 
Figure. If the proximate canons are applicable directly to all 
syllogistic moods, reduction is unnecessary. 

Order of the Premises. Many logicians have inverted the 
order of the premises, commencing with the minor. Thus — 
All X is Y 
AllYisZ 
All X is Z. 
This is the form that seems most convenient and convincing, 
in a chain of reasoning, as in the Sorites. It suits the particu- 
lar form of the syllogistic axiom, expressed by * the mark of a 
mark is a mark of the thing ; ' X is a mark of Y, Y is 
a mark of Z ; hence X is a mark of Z. It, however, disguises 
the genuine type of Deductive Reasoning, which ought to be 
exhibited in the standard syllogism, even, if we depart from it 
in the other figures. The universal proposition is rightly put 
forward as the foundation of the reasoning, to which should 
follow the applying premise, or the minor. In the moods of 
the 2nd, 3rd, and 4th Figures, inversion of premises occurs as 
one form of departure from the First or regular figure. 
Aristotle's mode of writing Barbara is — 
A is predicated of all B 
B is predicated of all C 
A is predicated of all C — 
where the minor is given first, and the propositions inverted 
in the wording ; * A is predicated of all B/ is the same as All 
Bis A. 

6. The ^Inemonic Lines of the Syllogism contain the 
statement of the different moods, with the manner of reduc- 
ing to the First Figure, those of the three last Figures. 

To each of the moods, as described, a technical name has 
been appended, Barbara, Celareut, &c. These words have 



143 THE SYLLOGISM. 

ted for showing the constituent propositions of 

ml how the moods of the 2nd, 3rd, and 4th 

may bo transmuted into moods of the 1st Figure ; as 

actually gone through in the foregoing explana- 

The nanus are made up in lines of Latin hexameter verse. 
AiBOAg artificial aids to memory, they stand unrivalled: — 
1. bArbArA, cElArEnt, dArll, fErlOque, prioris. 

ArE, cAmEstrEs, fEstlnO, bArOkO, secundae. 
. 3. tertia, dArAptl, dlsAmls, dAtlsI, fElAptOu, 

LOkArdO, f ErlsO, habet : quarta insuper addit. 
; 4. brAmAntlp, cAmEnEs, dlmArls, fEsApO, frEsIsOn. 
h of these names represents a mood ; the three capital 
s in each standing for the three propositions, as symbo- 
in their Quantity and Quality by the forms A, E, I, 0. 
Of the smaller letters, or consonants, r, n, t, are meaningless 
or dumb letters. The consonants that commence each name 
— />, c, c/, /—indicate the moods in the First Figure that the 
d moods in the other Figures are reduced to ; Bramantip 
• luced to Barbara, Cesare to Celarent, and so on. The 
consonants m, *, p, and k, which signify the processes of Reduc- 
tion : m indicating that the premises have to be transposed ; 
s indicating simple conversion ; p conversion by limitation, or 
iccidens; -while h is the symbol of reductio ad impossibile. 
The application of each is to the vowel immediately preceding. 
Thus, in Bramantip : — 

All Z is Y 
AllYisX 
Some X is Z — 

we learn from m that to obtain the form of Barbara, the first 
mood of the First Figure, we must transpose the premises. 
And as we should then see ourselves entitled to conclude 'All 
X,' it has further to be signified by p, that to obtain the 
conclusion 'Some X is Z,' we must make a limited con ver- 
sion. So in Fesapo to obtain Ferio of the First Figure, we 
must convert E simply, and A by limitation. Although the 
method of reduction ad impossibile may be applied to any of 
the irregular moods, the letter h occurs only in two, Barolco 
and Bokordo, these being the only two that the logicians found 
irreducible by the processes of transposition and conversion. 
The rules or Canons of valid reasoning are variously 
L They are proximate, rules, being derived from the 
tumhunental axioms of all Deduction 



CANONS OF THE SYLLOGISM. 149 

Common Canons. — These are six in number.* 

(1) Every Syllogism has Three, and only three, Terms. 

(8) There must be Three, and only three, Proporitiam. 

(3) The Middle Term must be distributed once, at least, in the 
premises. 

That is to say, the Middle Term must be a universal in one 
or other of the premises. It must be the subject of a univir- 
sal proposition (All Y is Z, No Y is Z), or else the predicate of 
a negative proposition No X is Y, Some X is not Y. As the 
subject of a particular proposition (Some Y is Z, Some Y is 
not-Z), and as the predicate of an affirmative proposition (All 
X is Y, Some X is Y), the middle term Y is particular, or un- 
distributed. 

By a reference to the nineteen valid syllogisms, it will be 
seen that in each of them the middle term is distributed once 
in the premises. Thus, in the First Figure throughout, it 
is the subject of the major, which is a universal ( All Y is Z, 
No Y is Z). This is as it ought to be in the standard syl- 
logism. In the Second Figure, it is distributed three times 
in the major, and once in the minor (Some X is not-Y). In 
the 1st, 2nd, 4th, and 5th moods of the Third Figure, it is 
distributed in the minor; being also distributed in the major, 
in the 1st and 4th. In the Fourth Figure, it is distributed in 
the minor, iu all the moods but the last. 

In the following couples, there is no distribution of the 
middle term (Y), and consequently none of the couples could 
6tand as premises in a valid deduction. 

All Z is Y Some Z is Y All Z is Y 

All X is Y Some X is Y Some Z is Y 

Some Y is Z, Some Y is not Z All Z is Y 

All X is Y, All X is Y Some Y is not X. 

A pretended syllogism, in such forms as these, or any form 
where the rule does not hold, is said to exemplify the fallacy 
of undistributed middle. 
Such are the following : — 

Some Y is Z Some men are kings. 

All X is Y All cooking animals are men. 

All X is Z All cooking animals are kings. 

Other examples will occur afterwards. 

(4) No term undistributed in the premises must be distributed in 
the conclusion. In other words, there must not be a greater 

* After WTiately, who gives them as a condensation of the twelve 
canons of Aldrich. 



150 THE SYLLOGISM. 

quantity attaching to any term in the conclusion, than is 
attached to the same term in the premises. If X be particular 
in the premises, so must it be in the conclusion ; the same with 
/, Tins condition, likewise, is fulfilled in the valid syllogisms. 
Thus : — 

AllYisZ NoYisZ. 

All X is Y Some X is Y. 

All X is Z Some X is not Z. 

In the first of the two, the subject of the conclusion is 
universal in the minor premise, and may therefore be universal 
id the conclusion ; in the second, it is particular in the minor, 
and must be particular in the conclusion. Iu both, the predi- 
cate of the conclusion is particular in the premises, and must 
be particular in the conclusion. So if, in Darii, a universal 
conclusion were drawn, it would be invalid. 
All Y is Z All men are mortal. 

Some X is Y Some extended things are men. 
All X is Z All extended things are mortal. 

We may have premises, free from the last-named vice of 
undistributed middle, yet made to yield a false conclusion by 
overstepping the present rule, or raising a term of particular 
quantity, in the premises, to the rank of universal quantity 
in the conclusion. To this error is given the name, Illicit 
process ; and according as the unduly extended term occurs in 
the major or in the minor premise, the error is called illicit 
process of the major or illicit process of the minor. 

In the foregoing instance, the illicit process is in the minor. 
^\ e give an instance of illicit process of the major. 
A11Y is Z All men are fallible. 

Some X is not Y Some beings are not men. 
No X is Z No beings are fallible. 

The major term * fallible,' being the predicate of an affir- 
mative proposition, is particular or undistributed ; in the con- 
clusion, it is the predicate of a negative proposition, and is 
t here fore distributed. 

(o.) There can be no conclusion drawn from negative premises. 
No Y is Z No men are gods 
No X is Y No trees are men 
do not supply the materials for a deductive inference. The 
n of this is already apparent from what has been said as 
to the applying proposition, which must always affirm. To 
know only that two things are each excluded from a third 
thing is to know nothing concerning their mutual relation. 

I If one premise he negative, the conclusion must be negative, 

' - • i * 

y K 



' 



HAMILTON'S CANONS. 151 

This is illustrated throughout; the scries of valid syllo ri 
If one premise be negative, all that is predicated coneerning 

one ot the terms is its exclusion in whole or in part from the 
middle term : we cannot, therefore, conclude through the 
medium of the middle term anything about its total or pi 
co-extension with the other term. 

In order to facilitate the detection of unsound syllogisms 
the two following rules, directly deducible from these canons] 
are also enounced. 

A. There is no inference from particular premises. 
Some Y is Z ' Some Y is Z 
Some X is Y Some X is not-Y 
give no conclusion. The first example contains an undistri- 
buted middle ; and the weakest inference drawn from the 
second (Some X is not Z) would contain an illicit process of 
the major. 

> B. If one premise is particular, the conclusion must he par- 
ticular. 

As in Dam, Ferio, &c. 

Any attempt to extract a universal conclusion where both 
premises are not universal would incur either undistributed 
middle or illicit process. 

This last canon, and aho the Sixth, are embraced in one 
statement — ' The conclusion always follows the weaker part/ 
8. Hamilton's Canons. These are three in number. The 
first contains the 1st and 2nd of the foregoing list (Three 
Terms and Three Propositions). The two others are as 
follows : — 

II. Of the Premises, the Sumption must in Qaantity be 
definite (i.e. universal or singular) ; the Subsumptioa in 
Quality affirmative. 

As Hamilton means by the Sumption the universal or 
ground proposition, and by the Sabsumption, the applying or 
subsuming proposition, this is declaring the characters of the 
standard syllogism. It appears that, through all the mutations 
of syllogistic moods, there must always be one nniv. 
proposition (or else a definite singular;, and one affirmative 
proposition. (The meaning of the alternative, a singular propo- 
sition will appear afterwards). 

III. The conclusion must correspond in ouality with the 
Sumption, and in quantity with the Subsuraption. 

Whatever be the quality of the Universal or ground propo- 
sition, that must be the quality of the conclusion ; the one 



152 THE SYLLOGISM. 

being affirmative the other is affirmative ; the one negative, 

mntity of the Applying proposition is the trne 
of the conclusion; universal giving universal, and 
particular giving particular. 

These two rules of Hamilton's are given as the equivalent 
for Whatdy's four last They have the advantage of placing 
in a due prominence the fundamental structure of deductive 
reasoning, which is altogether invisible in the foregoing canons; 
but they arc not readily applicable to the more distorted 
figures. Before using them, we must first discover which term 
contains the sumption, and which the subsumption ; and for 
this, we must refer to the directions given respecting the 
irregular moods. In short, we must first redress the inver- 
sions and distortions of the irregular moods, which is substan- 
tially to go through the process of reducing each to the first 
figure. 

9. The rides of the syllogism given in the form of separate 

canons for each figure. For the First or standard Figure, 

the canons of Hamilton are the most suitable expression. 

each of the other Figures, special canons may be 

framed according to the nature of the Figure. 

Thus, in the second Figure, it can be shown that, 

( 1 ) One premise is negative. 

(2) The major premise is universal. 
The proof is easy. (1) If both premises were affirmative, 

the middle term being the predicate of both premises, it would 
be undistributed. 

Again, (2) if the major were particular, the weakest conclusion 
that could be drawn, Some X is not Z, involves illicit process 
of the major. 

It follows from the first of the two rules (One premise must 
be negative) that, in this Figure, it is possible to prove negative 
conclusions only. 

In the Third Figure, the canons are, 

( 1 ) The minor premise is affirmative. 

(*2) The ctmclusion is particular. 

he minor premise were negative, the conclusion must be 
tive, and the major term affirmative, which would involve 
an illicit process of the major. 

n:, the conclusion must be particular, whether the 
syllogisms be affirmative or negative. 

The minor premise being affirmative, there cannot be a uni- 



SPECIAL CANONS OF THE FIGURES. 15H 

rersal affirmative conclusion without illicit minor. In a uni- 
versal negative conclusion both terms are distributed : and 
they cannot both be distributed in the premises, unless buth 
premises were negative, which could not be. 
In the fourth Figure, 

(1) Iii the negative moods, the major is universal. 

Some Z is not Y, Some Z is Y 

All Y is X, No Y is X 

could not yield even particular conclusions, without illicit 
process of the major* We should have to infer-;— Some X is not 
Z : and Z is undistributed in the premises in consequence of 
the particularity of the major. 

(2) If the major is affirmative, the minor is universal, 

A particular minor to an affirmative major would give 
All Z is Y, All Z is Y 

Some Y is X, Some Y is not X 

both forms containing undistributed middle. 

(3) If the minor is negative, both premises are universal. Try 

All Z is Y, Some Z is Y, 

Some Y is not X, No Y is X. 

There is, in the first form, undistributed middle ; and in the 
second, the weakest conclusion, Some X is not Z, contains 
illicit process of the major. 

This rule is implied in the two preceding. By the First 
rule, the Major is universal, because the mood is negative. By 
the Second rule, the Minor is universal, because the major is 
affirmative. 

(4) If the minor is affirmative, the conclusion is particular. 
With minor affirmative, we have — 

All Z is Y, No Z is Y 

All Y is X, All Y is X, 

In both cases, a universal conclusion would be attended with 

illicit process of the minor. 

10. That the valid moods are those above given, and no 
more, is shown by testing all the other possible moods ac- 
cording to the syllogistic canons. 

The possible moods may be arrived at by computing the 
possible groups of threes that can be made out of the four pro- 
positional forms — A, I, E, O. Now, taking the premises alone, 
there are sixteen different couples that can be made from these 
four letters. 

A, A I, A E, A 0, A 
A, I (1,1) E,I (0,1) 



154 TI1E SYLLOGISM. 

A,E I,E (E,E) (0,E) 
A, O (I, 0) (E, 0) _ (0, 0). 
Of these sixteen forms, we can reject at once, as inad- 
ble, first, those that have both propositions particular— 
10 1, 0. We can farther reject those that have 
both negatito— B E, E 0, O E (0 is rejected on the pre- 
vious ground). Alter these seven rejections, there are nine 
forma remaining. 

a farther sifting, two methods are open to ns. First, 
a try whether every one of the nine couples may stand as 
premises to conclusions of all the forms, A, I, E, O. 

A, A, A (A, I, A) (A, E, A) (A, 0, A) 
A, A, I A, I, I (A, E, I) (A, O, I) 

(A, A, E) (A, I, E) A, E, E (A, 0, E) 

(A, A, O) (A,I,0) ! A, E, O A, 0,0 

and so on through the remaining five forms. 

Now, by applying the canon that requires a particular con- 
clusion when one of the premises is particular, we exclude two 
in the second column — A I A, A I E, and two in the fourth — 
A A, A E. By applying the canon that requires a nega- 
tive conclusion when one of the premises is negative, we ex- 
elude, in the third column, A E A, A El; in the fourth 
column, A I (also A A excluded on the previous ground). 
Although no express canon is laid down requiring an affirma- 
tive conclusion from affirmative premises, such canon could be 
proved to be valid ; and by means of it, two exclusions would 
be made in the first column— A A E, A A 0, and one farther 
exclusion in the second. Hence, of the sixteen forms, six only 
survive these successive purgations. By a similar operation, 
extended to the remaining twenty forms, it would appear that 
there are in all twelve forms admissible ; — 

AAA, AAI, AEE, AEO, All, AOO 
EAE, EAO, EIO, I A I, I E O, O A O. 
If these twelve forms were each admissible in all the Figures, 
there would still be forty-eight valid syllogisms. But, by 
stating them under the successive figures, their ranks are 
thinned still farther. Thus, in the First Figure, A A I and 
A E are superfluous because they infer a smaller conclu- 
sion when a larger could be drawn ; with the premises A A, 
ui infer A {Barbara) ; with A E, we infer E (Celarent). 
Ot the remaining ten, six would involve violations of funda- 
■ d canons, as may be seen by expressing them in full 
1 wo examples are enough. Thus, AEE gives- 
All Y is Z All men are mortal 



SIFTING OF THE VALID MOODS. 

No X is Y No molluscs are men 

No X is Z No molluscs are mortal 

which contains illicit process of the major. The same would hap- 
pen under a particular conclusion, as in A, E, O. Again, I, A, 1-- 
Some Y is Z Some iishes are sharks 

All X is Y All salmons are Iishes 

Some X is Z Some salmon are sharks — 

has the middle term undistributed. 

By operating in this manner, we reduce the valid moods of 
the First Figure to the four formerly given — A A A, E A E 
A 1 1, E I O. 

The same process repeated for the remaining figures has 
the result of reducing the admissible forms to those actually 
given in the scheme of the syllogism. 

The other method of elimination is to apply the special 
canons of the figures to the nin8 forms of unobjectionable 
premises, A A, A I, &c. By the canons of the standard syllo- 
gism, the major is universal and the minor affirmative ; whence 
the forms, A E, A 0, I A, O A, are rejected at once ; and there 
remain only the four, A A, A I, E A, E I, corresponding to the 
four moods of the First Figure. For the Second Figure, the 
canons (One premise is negative ; the major is universal) 
exclude A A, A I, I A, I E, O A ; leaving A E (Camestres), A 
XBaroho), E A (Cesare), E I (Festino). For the Third Figure, 
the first canon (The minor is affirmative) excludes A E, A 0, 
I E ; and there remain A A (Darapti), A I (Datisi), I A (Disa- 
mis), E A (Felapton), E I (Ferison), A (Bokardo). 

For the Fourth Figure, the first canon (In the negative 
moods, the major is universal) excludes IE, OA. The second 
canon (If the major is affirmative, the minor is universal) 
excludes A I, A O. The remainder are A A (Bramantip), A E 
(Camenes), I A (Dimaris), E A (Fesapo), E I (Fresisou). 

AXIOM OF THE SYLLOGISM. 

11. Logicians have aimed at reducing the whole of the 
special canons or rules of the Syllogism to one comprehen- 
sive Law or Principle. 

The oldest form of this principle is that named the 
Dictum de omni et nullo. ' Whatever is affirmed or denied 
of a class, is affirmed or denied of any part of that class/ 

As stated, this maxim seems merely one of the forms of Im- 
mediate Inference : — 'all men are mortal/ hence * this man, 
ten men, some men, are mortal/ This, however, is not the 



* 



|56 AXIOM OF THE SYLLOGISM. 

form actually assumed by the syllogism. We have to prove 

some object is mortal, not expressly named a man, but 

rnated by some other title, as 'king. 9 We cannot say 

mortal,' therefore 'kings are mortal;' such aninfer- 

can he made only through an intermediate assertion, 

4 kings are men.' 

Another defect has been pointed out in the dictum : namely 
that it proceeds upon the old erroneous view of a proposition, 
the reference of a thing to a class. This, however, might be 
got over by understanding ' class ' to mean the class indefinite, 
marked by the connotation of the class name. Practically, 
such must be the case ; we have no means of pointing out the 
class l men/ except as the possessors of human attributes. 

Considering the dictum as the basis of all Deductive Reason- 
ing, we might amend it thus : — 'whatever is true of a whole 
(class indefinite, fixed by connotation), is true of whatever 
thing can be affirmed to come under or belong to the class (as 
ascertained by connotation). ' This supposes the need of a 
second affirmation, the minor proposition, and is no longer an 
immediate inference. 

12. The defects of the dictum are supposed to be remedied 
by this form : — 

Attributes, or Things, co-existing with the same Attri- 
butes or Things, co-exist with one another (Affirmative). 

If the attributes of a king co-exist with those of a man, and 
the attributes of a man co-exist with the attribute * fallibility/ 
the attributes of a king co-exist, or co-inhere with the attribute 
fallibility. 

There is a close resemblance between the present form and 
the mathematical axiom— Things equal to the same thing, are 
equal The two are alike axioms of mediation; they connect 
two things by a common third. 

The negative form is stated thus :— ' One thing co-existing 

with a second thing, with which second thing a third thing 

does not co-exist, is not co-existent with that third thing;' 

winch resembles the axiom— Things unequal to the same thing, 

unequal. u ° 

is mode of stating the axiom has often been adopted by 

uins :— JSoia notce est nola rei ipsius ; Things that agree in 

»me third, agree among themselves. For the negative 

^nn~r q ,u f jnans notce, repugnat rei wsi ; Things whereof the 

one agrees, the other does not agree, with the same third, do 

not agree among themselves. 



NOTA N0T7E. 157 

The advantages of the form aro indicated by tho remarks 
already made. It gives very great prominence to tho fac 
mediation in Deductive Inference, and thus draws a broad lino 
between it, and Immediate or Apparent Inference. It also 
accommodates itself to such a case as Darapti, with a singular 
subject, thus, 

Socrates was wise. 

Socrates w r as poor. 

Some wise men have been poor. 
Now, the treating of a Singular proposition as a universal, 
which is necessary to make the above a regular syllogistic 
form, has always seemed a great anomaly in the syllogism. 
Indeed, it is a subversion of the theory of Deductive Reasoning, 
as supposed to consist in the application of a general or uni- 
versal principle to a case coming under it. But, if we accept 
the present form of the axiom, the above syllogism is rendered 
with apparent ease. 'Wise' co-exists with * Socrates ;' 'Poor* 
co-exists w 7 ith Socrates ; therefore ' Wise ' and * Poor' co-exists 
with one another ; that is, ' Some wise persons are poor.' 

A farther advantage of the same form consists in following 
out the the * Connotation ' theory of Propositions. The exten- 
sion of the several propositions is completely banished from it, 
and nothing but Connotation or Comprehension left. It is no 
longer 'all A is B,' but the attribute A co-exists with the 
attribute B,' and so on. From the same cause, a seeming facility 
is given in chains of reasoning, which can be rendered thus : 
— A is a mark of B, B of C, C of D ; wherefore A is a mark 
ofD. 

Notwithstanding so many advantages, this form of the axiom 
now described is unworkable as a basis of the syllogism. The 
fatal defect consists in this, that it is ill adapted to bring out 
the difference between total and partial coincidence of term?, the 
observation of which is the essential precaution in syllogizing 
correctly. If all terms were co-extensive, the axiom would flow 
on admirably ; A carries B, all B and none but B ; B carries 
C in the same manner ; whence A carries B, without limita- 
tion or reserve. But, in point of fact, we know that while A 
carries B, other things carry B also, whence a process of limita- 
tion is required, in transferring A to C through B : — A (in com- 
mon with other things) carries B ; B (in common with other 
things) carries C ; whence A (in common with other things) 
carries C. The axiom provides no means of making this limi- 
tation ; if we were to follow A literally, we should be led to 
suppose A and C co-extensive : for such is the only obvious 



258 AXIOM OF THE SYLLOGISM. 

ing of 'the attribute A coincides with the attribute 

lesfl the predicate is quantified, as Hamilton recommends, 
ropogitional form in Extension— ' all men are mortal/ 
cplicitly suggest that ' men are but a part of mortals ;' 
d readily conceive the fact when reminded of it ; the 
extent of ' mortal beings ' is greater than the extent of ' men.' 
the proposition stated in pure connotation or comprehen- 
ds the present axiom requires, — ' the attributes of men co- 
with the attribute mortality 1 — is difficult to adapt to the 
f.tcuhat mortals are more numerous than man. We should 
to make a still greater circumlocution : — the attributes 
of men co-exist, but are not the only attributes that co-exist, 
with the attribute 'mortality.' So, the attributes of a king 
>t, but are not the only attributes that co-exist, with the 
attributes of men. The conclusion would then be — The 
attributes of a king co-exist, but are not the only attributes 
that co-exist, with the attribute ' mortality.' Now, as the 
axiom 'attributes co-existing with the same attribute co-exist 
with one another' does not suggest these necessary limita- 
tions, it is not, as worded, an explicit basis for the syllogism. 

It is only the same objection, otherwise put, that the axiom 
does not accommodate itself to the type of Deductive Reason- 
ing, as contrasted with Induction — the application of a general 
principle to a special case. Anything that fails to make pro- 
minent this circumstance is not adapted as a foundation for the 
syllogism. 

The scientific processes of Induction and Deduction are 

habitually conceived on the basis of Extension ; it is only thus 

that we readily appreciate the greater or less generality of 

propositions. Hence the proper view of the syllogism, as of 

the notion and the proposition, is to base it on Extension, but 

to determine the extension by Connotation or Comprehension. 

1 All men are mortal ' is best understood as the concrete 

population of human beings, defined and determined by the 

attributes of humanity. This double point of view com- 

with all the exigencies of reasoning, and is not advan- 

usly surrendered in favour of the statement of propositions 

in pure comprehension. 

The result of the comparison of the two axiomatic state- 
That the Dictum de omni et nuilo, properly guarded, 
St suitable and exact representation of the essential 
ire of Deductive Reasoning or Syllogism. 
Tlu. case of Rin^uW Propositions, held for the nonce to be 



SINGULAR PROPOSITIONS. 159 

universal, is a grave exception to the Deductive process as wo have 
uniformly described it. On examining such cases, however, wo 
may see good reason for banishing them from the syllogism. ' Let 
as take the example already quoted : — 
Socrates is poor 
Socrates is wise 
Some poor men are wise. 
Properly, the conclusion is, ' one poor man is wise.' Now, if 
1 wise,' ' poor,' and * a man,' are attributes belonging to the mean- 
ing of the word Socrates; there is then no march of reasoning at 
ali. We have given, in Socrates, inter alia, the facts 'wise/ 'poor,' 
and ' a man,' and we merely repeat the concurrence, which is 
selected from the whole aggregate of properties making up the 
whole, ' Socrates.' The case is one under the head ' Greater and 
Less Connotation,' in Equivalent Propositional Forms, or Immedi- 
ate Inference. 

But the example in this form does not do justice to the syllogism 
of singulars. We must suppose both propositions to be real, the 
predicates being in no way involved in the subject. Thus ; — 
Socrates was the master of Plato 
Socrates fought at Delium 
The master of Plato fought at Delium. 
It may fairly be doubted whether the transitions, in this 
instance, are anything more than equivalent forms. For the 
proposition, ' Socrates was the master of Plato, and fought at 
Delium,' compounded out of the two premises, is obviously nothing 
more than a grammatical abbreviation. No one can say that there 
is here any change of meaning, or anything beyond a verbal 
modification of the original form. The next step is, ' the master 
of Plato fought at Delium,' which is the previous statement cut 
down by the omission of * Socrates. ' It contents itself with 
reproducing a part of the meaning, or saying less than had been 
previously said. The full equivalent of the affirmation is 'the 
master of Plato fought at Delium, and the master of Plato was 
Socrates ;' the new form omits the last piece of information, and 
gives only the first. Now, we never consider that we have made 
a real inference, a step in advance, when we repeat less than we 
are entitled to say, or drop from a complex statement some portion 
not desired at the moment. Such an operation keeps strictly 
within the domain of Equivalence or Immediate Inference. In no 
way, therefore, can a syllogism with two singular premises be 
viewed as a genuine syllogistic or deductive inference. 

13. The Proof of the Axiom is uncontradicted experi- 
ence. 

The Dictum is not a mere rule of consistency, exacting the 

admission, in equivalent forms, of all that has been conceded 

in one form. It is a mediate process, and the mediation has 

to be justified by an appeal to the facts. As far as proof goes, 

8 



ICO AXIOM OF THE SYLLOGISM, 

nn bles in character the second form above given— 4 Things 
dating with the same thing, co-exist,' and the math ema- 
m 4 Things equal to the same thing are equal/ All 
the three principles stand upon the same foundation; some 
philosophers refer them to intuition, others to experience ; but 
the mode of proof for one is the mode for all. ^ The dictum 
m cms to approach nearest to a mere rule of consistency; yet 
the fact of mediation makes all the difference ; ' the identical 
of an identical is identical ' is a new step and needs a new jus- 
tification. Nobody would accept even so obvious an inference 
— as \ men are mortal, kings are men. kings are mortal/ with- 
out first verifying upon examples the peculiar kind of transi- 
tion involved. We aro so alive to the snares lurking in the 
most obvious and plausible forms of language, that we do not 
trust any of them without the check of actual trials. Nothing 
could seem more satisfactory than ' A co-exists w r ith B, B with 
C, therefore A co-exists with C wholly and unconditionally/ yet 
until we have elaborately fenced the operation against the 
simple conversion of a universal, the conclusion is unwarranted. 

Viewing together the Mathematical axiom of Equality and the 
axiom of the Syllogism, Mr. de Morgan remarks : — ' In both there 
is a law of thought appealed to on primary subjective testimony of 
consciousness ; ' * equal of equal is equal ' in the one ; * identical of 
identical is identical' in the other. The two laws are equally 
necessary, equally self-evident, equally incapable of being resolved 
into simpler elements. 

14. There are other modes of stating the Axiom. Hamil- 
ton has two forms. The first is for what he calls Informal 
reasoning:— In so far as two notions (notions proper or 
individuals) either both agree, or one agreeing the other 
does not, with a common third notion ; in so far, these 
notions do or do not agree with one another. 

This is simply one way of wording the Nota noice, and is 
liable to the objections urged against that form. There is no 
provision for distinguishing total from partial agreement, and 
therefore no basis for the working of the syllogism. The 
words * agreement ' and ' disagreement ' are less apt than ' co- 
existence ' and 'non-coexistence' for expressing the axiom ; 
t hey have the defects inherent in the * judgment ■ theory of 
Propositions. & J 

15. For the Figured Syllogism, where the terms are re- 
lated as subject and predicate of propositions in a given 



HAMILTON'S FORMS. 1G] 

order, Hamilton enounces this form : — What worse 
lation of subject and predicate subsists between eithe 
two terms and a common third term, with which on 
least, is positively related ; that relation subsists between 
the terms themselves. 

The peculiar phraseology * What worse relation ' is a man- 
ner of saying that the conclusion must carry the weakest re- 
lationship signified by the premises. If there be a negative in 
the premises, there must be a negative in the conclusion ; if 
there be particularity in the premises, there must be particu- 
larity in the conclusion. The same thing is otherwise ex- 
pressed — * The conclusion must follow the weaker part.' 

This is the Axiom given in Extension, and is in accordance 
with the Dictum, although not stated with the same generality. 
It more resembles one of the canons for working out the syllo- 
gistic details, itself resting on the Dictum, 

16. The first of Hamilton's two forms is expressed 
otherwise thus (Thomson) : — The agreement or disagree- 
ment of one conception with another, is ascertained by a 
third conception, inasmuch as this, wholly or by the same 
part, agrees with both, or with only one of the conceptions 
to be compared. 

This form appears to be based upon Comprehension, or the 
Nota notce, but endeavours to introduce the limitations requisite 
for discriminating total and partial quantity. The phraseology, 
however, — 4 conception, &c.' — is ambiguous ; it may express 
either extension or comprehension — 'men* or the attributes 
4 human.' If, taken in extension (which is most probable), is 
closely reproduces Hamilton's second form, and puts stress 
upon the difference between total and partial coincidence. 
Nevertheless, it does not rise to the sweep of the Dictum, 
in declaring the paramount circumstance of deductive reason- 
ing, — the carrying out of a general law to particular cases. 

If * conception ' means attributes, comprehension, or conno- 
tation, the phraseology would indicate Hamilton's syllogism of 
Comprehension, and would not suggest the common syllogism. 
The attributes * king ' and the attribute * mortal ' agree (better 
* coincide ') by agreeing (coinciding) with the same part of the 
attributes * human.' Hamilton's syllogism is more explicit ; 
thus — The attributes * king ' contain the attributes k man ;' 
the attributes * man ' contain the attribute l mortal ;' the 
attributes * king ' contain the attribute * mortal.' 



IQ2 AXIOM OF THE SYLLOGISM. 

17. In the comprehensive scheme of De Morgan, the 
axiom is a generalization of many special axioms. The 
syllogism is treated as the composition of two relations 
into owe ; the axiom is ' the relation of a relation is a rela- 

compounded of the two. 
The truth of this is seen, and its application controlled, by 
the special instances of relationship. One of these instances is 
the axiom of the common syllogism. Others are the mathe- 
matical axioms, * Equal of equal is equal/ and 'greater of 
mater is still greater ' (a fortiori). Among more special in- 
stances are ' antecedent and consequent/ 'ancestor and 
descendant. 

18. It has been supposed by some that the common 
axiom, as expressed by the ' dictum de omni et nullo/ is 
a consequence of the Laws of Thought (Identity, Contradic- 
tion and Excluded Middle). 

Hamilton maintains that categorical syllogisms are regulated 
by the fundamental laws of Identity and Contradiction. He 
interprets the law of Identity as the identity of a whole and 
the sum of its parts, whence he considers it right to infer 
that what belongs to a whole belongs to its part. Mr. Mansel 
agrees with Hamilton in referring the syllogistic laws to the 
same principles. 

The effect of this doctrine is to abolish the difference be- 
tween Immediate and Mediate Inference, by bringing mediate 
inference under Immediate, or under the law of Consistency. 
On the face of it, the supposition is unlikely ; and accordingly 
it has been denied by other logicians. Thus, Mr. de Morgan 
(Syllabus, p. 47) remarks of the attempts to reduce the syllog- 
ism to the three so-called Laws of Thought, ' When any one 
attempts to show how. I shall be able to judge of the process; 
is, I find that others do not go beyond the simple asser- 
tion, and that I myself can detect the pet itio principii in every 
one of my own attempts/ 

The law of Consistency requires us to concede that what is 

true of a class is true of every individual in the class; 'all men 

are fallible,' ' the half of men are fallible, this man is fallible ' ; 

there is no transition, it is the same fact, repeated only to 

i extent. But when we say < kings are men/ * kings are 

fallible, there is a transition to a different subject, a subject 

present to the mind as a part of the original whole, but 

brought under it by a second assertion. Now a distinct axiom, 



DERIVATION OF SPECIAL CANONS. 163 

is needed to transfer the attribute nnder this now case. Tho 
axiom may be in its nature self-evident, but the conclusion* 
regulated by it are not identical with either of the pre 
an immediate inference, properly so called, is identical with tho 
original form. 

19. The special canons of the Syllogism are derivable 
from the Axiom. 

(1) It easily follows from the Diefum, as explained, that 
there are three terms, and no more. There is a Universal Pro- 
position containing a subject and a predicate, an applying or 
Interpreting proposition, adding a third term, and repeating 
one of the terms of the universal: — All or no Y \s Z, All X 
is Y. The conclusion contains no new term — All X is Z. 
Whence there are three terms in all. 

(2) The same examination shows that there are three and 
no more than three propositions ; — the Universal, the Inter- 
preting Proposition, and the Conclusion. 

(3) The third special canon is — ' The middle term must be 
distributed once in the premises.' Distribution or Universal 
Quantity in the middle term is essential to the total coincidence 
or non-coincidence of at least one of the other terms with the 
middle term ; without which the two extreme terms could not 
be shown either to coincide, or not to coincide, in whole or in 
part. * Some men are fallible/ 4 kings are some men,' — would 
not bring about a coincidence between ' fallibility' and * kings ;' 
one portion of men might be fallible, and a different portion 
might be kings. This is obviated if fallibility adheres to all 
men ; it must then adhere to whatever objects are found to be 
men. 

(4) The fourth special canon is — ' No term undistributed 
in the premises must be distributed in the conclusion.' It may 
be brought under the Dictum thus : — The distribution of a 
term in the conclusion means universal or total coincidence 
with the other term of the conclusion ; — * All X is Z ' means 
that X is wholly coincident with, wholly included in Z. Now 
X and Z are brought together by a middle term Y ; and if X 
did not wholly coincide with Y in the first instance, it could not 
be transferred, in total coincidence, to Z. If we had only some 
X is Y, even although all Y is Z, we could not declare all X to 
be Z. There is carried over to Z only so much of X as goes 
with Y ; if that be the whole, the whole is carried ; if a part, 
part is carried. If ' all men are fallible,' and ' some beings are 
men,' only some beings are fallible, namely, as many as are men. 



1(34 AXIOM OF THE SYLLOGISM. 

(5) ' From negative premises, there is no inference.' Nega- 
preraises do not comply with the essential fact of the in- 
terpreting proposition, which is to declare that a given case 
comee under the sweep of the rule. Whether the universal 
Urinative or negative, the applying proposition must, from 
in iv, be affirmative. No Y is Z,no X is Y, could not be 
the means of bringing X under Z, or of bringing these two 
u*n us together in a conclusion ; we could not, from such pre- 
mises, infer even No X is Z. 4 No matter is destructible ' re- 
quires to be followed up with * ether is matter ' to prove that 
1 no ether is indestructible.' 
(0) 4 It' one premise be negative, the conclusion is negative/ ex- 
es exactly what happens in the negative form of the axiom. 
In the enlarged scheme of De Morgan, some of these rules 
are violated in appearance, but only in appearance. Thus 
from * two negative premises ' he draws a conclusion in the 
affirmative. This, however, arises from the elasticity of ex- 
pression allowed by the use of contrary forms. Every affirma- 
tive proposition may be given as a negative ; and there may 
be the semblance of negation, with the reality of affirmation 
in conformity with the axiom. Thus — 

AUYisZ = No Y is not Z. 
AUXisY = NoXisnotY. 
All X is Z All X is Z. 

20. The axioms — ' Equals added to equals, give equal 
sums/ and the argumentum a fortiori, if received as axioms 
in Logic, are distinct, from the axiom of the Syllogism, and 
must be independently proved. 

The argumentum a fortiori is represented thus : — If A is 
greater than B, and B greater than C, still greater is A than 
0. This, and the other axiom stated, are purely mathematical 
in their character; they serve for the comparing of quantities 
as equal or unequal. They rest on their own special evidence 
of fact. l 

It will be seen that Boole draws the Syllogism under the 
axiom that suffices for the reduction of equations. He assumes 
that the analogy of the logical method and the algebraical is 
•efficiently close to allow of the substitution. 

The conflicting opinions as to the evidence of axioms gener- 
ally, whether of logic, of mathematics, or of other sciences, will 
be discussed in a succeeding chapter. 



TESTING OF ARGUMENTS. 165 

EXAMPLES OF THE SYLLOGISM. 

21. The chief application of the theory and the forms of 
the syllogism is to detect fallacies in deductive reason 

There are certain forms of deductive reasoning or argument, 
that are specious to appearance, and fallacious in reality ; and 
the analysis of the syllogism is useful in disclosing the fallaci- 
ousness. 

22. The course of procedure, in dealing with an argu- 
ment in any way uncertain or perplexed, is as follows :— 

I. Ascertain what is the conclusion, or the point to be 
proved. State this distinctly in a proposition so as to dis- 
tinguish the Subject (miner term of the syllogism) and the 
Predicate (major term). 

II. Find out the middle term of the argument. In a valid 
syllogism there must be a middle term, and only one : and it 
must be something not occurring in the conclusion. 

III. Find out some proposition connecting the middle term 
with the major term ; this is the major premise of the syllogism. 
Also some proposition connecting the middle term with the 
minor term ; giving the minor premise of the syllogism. 

IV. The two premises and the conclusion being stated in 
form and order, the validity may be judged according to the 
laws of the syllogism. 

(1) If the deduction coincides with any of the valid moods, 
it is valid ; if not, not. 

(2) It being seen what Figure the argument comes under, it 
may be tested by the special canons of that figure. 

(3) The general canons of the syllogism may be applied to 
discover errors, if there be any such. 

Any one of these three modes may be adopted at choice ; 
inasmuch as each of them singly is conclusive. 

The easiest remembered mode of testing a syllogism, when 
once in form, is by the six general canons of the syllogism. 
Of these, the two that are most usually violated in sophistical 
reasonings are the 3rd (Distribution of the Middle Term) and 
the 4th (The quantity of the terms in the conclusion not greater 
than in the Premises). An argument with negative premises 
(o) would deceive no one. It would also be obvious, without 
much Logic, that one premise being negative, the conclusion 
must be negative (6). 

23. As an alternative, we may discard the consideration 



1C6 EXAMPLES OF THE SYLLOGISM. 

of the separate Figures, and reduce every argument at once 
standard form of Deduction. 

From the very nature of deductive reasoning, the conclusion 
rial application of some more general proposition. 
This more general proposition must be found in the premises ; 
it is the ground proposition ; in Hamilton's phraseology, the 
Sumption. There must also be found another proposition 
declaring its applicability to a particular case, namely, the 
given in the conclusion. These two indispensable proposi- 
tions may occur under distorted forms, which we must be able 
to redress by the methods already pointed out, that is, by 
obversion and conversion, as the case may be. Also, the 
conclusion may require to be obverted or converted, or both. 
uch methods, we may evade all the variations of figure, 
and come at once to the regular type of deduction. 

EXAMPLES. 

All men are mortal All Y is Z. — (A) ) 

No dogs are men ]STo X is Y. — (E) > 1st Fig. 

No dogs are mortal No X is Z. — (E) j 

(1) This syllogism is in the First Figure, but there is no 
mood in that Figure containing the propositions A, E, E. 

(2) Otherwise : The major term, mortal, is distributed in 
the conclusion, and not in the premises ; there is illicit process 
of the major. 

(S) Or lastly : It contradicts the canon of the normal syllo- 
gism, whereby the minor is declared to be affirmative. 
All planets are round All Z is Y. — A ) 
A wheel is round All X is Y.— A } 2nd Fi°\ 

A wheel is a planet All X is Z.— A J 

(1) There is no such mood in the Second Figure, 

(2) The middle term, ' round,' is undistributed. 

(3) There is a violation of the special canon of the Second 
Iigure— One premise must be negative. 

' Every honest man attends to his business ; this person 
attends to his business ; this person is an honest man/ This 
is the exact counterpart of the foregoing. The conclusion 
being this person is an honest man ;' the minor term is ' this 
person the major, « an honest man/ The middle term is 
attends to his business/ The major premise (major and 
middle), Every honest man attends to his business/ A ; the 
minor premise, •this man attends to his business/ A (a definite 



FALLACY OF CONVERSION. 1G7 

individual may be considered as either A or I). On any one of 
the three grounds given in the foregoing example, the reason- 
ing is fallacious. 

These two examples are regarded by logicians as of a type 
calculated to mislead, and therefore exemplifying the use of 
the laws of the syllogism. It is interesting to enquire what 
circumstance gives them their fallacious plausibilitv. With 
this view, we may proceed by the alternative method above 
pointed out, namely, by ascertaining whether these be the 
regular premises of deduction. 

To prove that a wheel is a planet, we must have a more 
general proposition, of which this shall be a particular case. 
Such a proposition would be 'all round bodies are planets:' 
We should then require an applying or subsuming proposition, 
namely, 'wheels are round bodies.' With these two proposi- 
tions, the conclusion would be legitimate, that wheels are 
planets. Looking at the premises given, however, we do not 
find a proposition corresponding to the first, or the general 
proposition. It is stated, not that ' all round bodies are 
planets,' but only that * all planets are round/ a different 
proposition. The confounding of the two is effected by the 
simple conversion of a universal affirmative; by arguing from 
'all planets are round/ that 'all round bodies are planets,' 
which we can do only if there are no round things but planets. 
In short, the fallacy, traced to its root, is a fallacy of conversion ; 
and if we are liable to be deceived by such syllogisms as the pre- 
sent, it is because we are liable to slip into this fallacy. There is 
something in the form of the universal affirmative that throws 
us off our guard ; from the expression All X is Y, we are apt 
to assume the co-extension of X and Y, unless cautioned and 
educated to the contrary. In cases where the co-extension 
exists, and only in such cases, could the argument in question 
give a sound conclusion. Thus — 
All matter gravitates. 
Air gravitates. 
Air is matter. 

Now, by the same process as before, it is shown that the 
general proposition needed for this conclusion is ' All gravi- 
tating things are matter,' which happens to be true, but is not 
justified by the assertion in the major, ' all matter gravitates ;' 
for there might be other gravitating things. 

So in the second example ' Every honest man attends to his 
business,' &c, we should require the terms ' honest man* and 
* attention to business ' to be co-extensive, which they are not. 



168 EXAMPLES OF THE SYLLOGISM. 

Whatever tendency we have to be deceived by such reasonings 

depends solely upon the intellectual weakness of presuming 

I tension of terms, in universal affirmations. 

Hume says:— 4 We have no perfect idea of anything but a 
percept ion . A substance is entirely different from a perception. 
We have therefore no idea of substance. ' 

The first step is to resolve the conclusion into its two terms. 
As often happens, in Logic, these terms are not the grammati- 
cal subject and grammatical predicate ; a transformation must 
be given to suit the tenor of the premises. Comparing the 
first proposition with the last, we see that the minor term, or 
subject of the conclusion, must be 'having an idea/ the 
major term is 'substance/ The affirmation is negative; 
literally, onr 4 having an idea ' is not true of substance. It is 
denied that substance is one of the things included under 
having an idea. The next point is to single out the middle 
term, namely, * perception/ Joined with the major and minor 
terms respectively, this yields as premises — 

No ' having an idea ' is not perception. 

All substance is not perception. 

No ' having an idea ' is true of substance. 
In the present form, the reasoning is wholly inadmissible ; the 
premises are both negative. We might, however, obvert the 
middle term 'perception/ and regard not-perception as the 
true middle (like changing l not wise ' into not- wise, or foolish). 
We have thus — 

No ' having an idea ' is not-perception E ' 

All substance is not-perception A 

No ■ having an idea ' is substance. E ] 
In this form the argument is sound. 

It is often desirable to express arguments of great subtlety, 
such as the present, in the standard form of deduction. The 
requisite transmutation would have to be effected thus. The 
conclusion, ■ " having an idea " is not true of substance/ is to 
be converted 'No substance is included in our having an 
idea. For this, the universal proposition would be a proposi- 
tion of denial more comprehensive than substance :— No 
not-perception is included in our having an idea. The minor 
is then, All substance is not-perception ; whence we conclude 
according to the regular form for the negative deduction. 
rrom ho middle term being a negation, however, this, can 
never be an easy form of argument ; and more especially so in 



No * having an idea ' is not-perception E \ 

All substance is not-perception A > 2nd Fig. (Cesare), 

No ' havinc an idea ■ is snl-vefanna 171 






EXAMPLES OF THE SYLLOGISM. 1G9 

the present argument, where perception is as wido as exist- 
ence, and has only a formal, and not a real obverse. 

Thus, then, we have, in the First Figure, as Cdarent 

Nothing that is not a perception (no not-perccption) can 

be perfectly conceived, E 

Substance is not a perception (a not-perception), A. 

Substance cannot be perfectly conceived. K 

'None but Whites are civilized; the Hindoos ore not 
Whites ; therefore they are not civilized/ 
In a syllogism thus : — 

No not- Whites are civilized E } 
The Hindoos are not Whites A >- (Celarent). 
The Hindoos are not civilized E ) 
A correct argument, the middle term being ' not- Whites/ for 
which the positive equivalent would be the remaining members 
of the Universe, * races of men ' (Black, brown, yellow, &c.) 
This would give a more intelligible form : — 

No communities of the black, brown, or yellow races are 
civilized ; 

The Hindoos are of the black or brown races. 
The Hindoos are not civilized. 

' Abstinence from the eating of blood had reference to the 
divine institution of sacrifices ; one of the precepts delivered 
to Noah was abstinence from the eating of blood ; therefore, 
one of the precepts delivered to Noah contained the divine 
institution of sacrifices ' (Whately). 

Although prolix in the wording, there is little distortion in 
this example. The minor term is obviously * one of the 
precepts delivered to Noah/ the major, * contained or had 
reference to the divine institution of sacrifices. f The middle 
term is ' abstinence from the eating of blood / and the arrange- 
ment is exactly as in the standard syllogism. 

* Few treatises of science convey important truths, without 
any intermixture of error, in a perspicuous and interesting 
form ; and therefore, though a treatise would deserve much 
attention which should possess such excellence, it is plain that 
few treatises of science deserve much attention.' (Whately). 

The conclusion gives as minor term ' few treatises of 
science/ as major ' deserve much attention.' The middle term 
is * convey important truths, &c/ The major premise, there- 
fore, is — 



170 EXAMPLES OF THE SYLLOGISM. 

All treatises of science that convey &c, deserve attention: 

minor promise— . 

I\ w treatises of science are works conveying important, &c. 

The conclusion— 

few treatises of science deserve attention {Dam). 

It was formerly remarked (p. 82) that for Some, in the minor 
term we may have— Few, most, many, one, two,— provided 
tl.al 'the same quantity is used in the premises and m the 
conclusion. 

* Enoch (according to the testimony of Scripture) pleased 
God ; but without faith it is impossible to please Him ; there- 
lure Enoch had faith' (Whately). 

The minor and major terms are obvious. The middle is 
'pleasing God/ The major premise is—* pleasing God is im- 
posaible without faith/ which is a circumlocution by way of 
expressing emphatically the proposition 'pleasing God is 
having faith ' — ' all persons that please God have faith/ The 
minor premise being 'Enoch pleased God/ the conclusion fol- 
lows from the regular type of deduction; 

It was said by some one during the Reform discussions of 
18G7 : — * Every reasonable man wishes the Reform Bill to 
I don't.' There was but one inference. The speaker 
was not a reasonable man (Camestres). This is a good example 
to show that an effective argument may be given out of the 
First Figure. 

If we follow the ordinary method of reduction in this case, 
we find ourselves in a difficulty. Camestres is usually reduced 
to the First Figure by transposing the premises and simply 
converting the original minor : if we do so in this case, we 
find a singular proposition in the major premise, which cannot 
be converted without doing great violence to the ordinary 
forms of language, and cannot stand as the grounding pro- 
position conceived as a general rule. The general rule in this 
is obviously the existing major — * Every reasonable man 
wishes the Reform Bill to pass.' But if we view this as the 
general rule, then we appear to have a negative applying pro- 
position — ' 1 don't.' Looking more closely at the premises, we 
hat the true nature of the predication is disguised. The 
major proposition is really negative, and the minor really affir- 
mative. The remedy for the distortion is to obvert the major 
into— k No reasonable man wishes the Reform Bill to fail ;' or 
4 No man that wishes the Reform Bill to fail is reasonable.* 






EXAMPLES OF THE SYLLOGISM. 171 

The minor when altered to correspond becomes — * I do ;' and 
we have a syllogism in Celarent, 

Another example of this same mood, Cam est res, illustrates 
the occurrence in ordinary reasoning of other syllogistic forms 
than the moods of the standard figure. We are presented with 
the assertion that 'No despotism is a good form of govern- 
ment/ and on asking the ground of such an assertion, are 
told — 'Every good form of government promotes the intelli- 
gence of its subjects, and no despotism does that* This is an 
argument in Camestres. 

Every good form of government promotes ) » 

the intelligence of its subjects. j- c m 

No despotism promotes, &c. Es 

No despotism is a good form of govern- ) . -p 
ment. J 

The above statement of the Major is the natural statement of 
the proposition ; the order of subject and predicate is such as 
a reasoner would naturally observe. That it promotes the in- 
telligence of its subjects is affirmed of every good form of 
government ; the order of the terms conforms to the usual 
arrangement of having the largest term in the predicate ; 
other agencies than good government promote the intelligence 
of the people. 

As in the former Camestres, this syllogism cannot be reduced 
to the First Figure by the process indicated in the Mnemonic 
letters without putting the real Major, or grounding proposi- 
tion, in the Minor place. We may retain the present order 
without violating the rule that the applying proposition must 
be affirmative. For the present major, affirmative in form, is 
obviously negative in its bearing ; while the minor, negative 
in form, is really of an affirmative nature, asserting that a 
despotic form of government possesses the character contem- 
plated in the ground proposition as precluding the title of 
good. By obverting the predicate of the major, the middle 
term, we manifest the real character of the premises : — 

No form of government that fails to promote the intelli- 
gence of its subjects is a good from of government. 

A despotism fails to promote the intelligence of its subjects. 

No despotism is a good form of government. 

In speaking of the general uses of the Figures, we remarked 
that the Third Figure is sometimes useful in making good an 
unobtrusive and timid contradictory. The three first moods 



172 EXAMPLES OF THE SYLLOGISM. 

hupply mild contraries to a universal negative ; the two last 
mild contraries to a universal affirmative. We give an ex- 
ample of each. 

Suppose a speaker to maintain absolutely and without 
vat ion that speculation is of no value. His position in 
il form is — * No speculation is valuable.' We subvert this 
xtort from the speaker a concession that his position is 
too extreme, when we obtain his assent to the two proposi- 
tions — 4 Some truths affecting human conduct are speculations', 
and 'All truths affecting human conduct are valuable.' These 
two propositions involve the sub-contrary of the extreme 
negative ; — namely, Some speculations are valuable. They are 
given in the order of subject and predicate natural to the 
occasion, and they fall into the Third Figure. They serve as 
premises either for Disamis, or Datisi, according to the order 
we observe in enouncing them. Thus : — 

Some truths affecting human conduct") jy 

are speculations ) 

All truths affecting human conduct \ A 

are valuable j Am 

Some speculations are valuable Is 

This is a syllogism in JDisamis. But it is to be observed that 
we invert the normal order of the major and minor terms in 
the conclusion. The most natural form is Datisi — thus : — 
All truths affecting human conduct ) -, A , 

flTfi vnlnnKlo > Q At 



are valuable 



J 



Some truths affecting human conduct 7 T 
are speculations j ** 

Some speculations are valuable I 

If our opponent should concede that all truths affecting 
human conduct are speculations, we should have a syllogism 
in Varaph In that; case, our partial contradiction would 
seem peculiarly bland, because our premises would then be 
superfluously strong, and we should have the appearance of 
remitting something in the conclusion. 

Our next example illustrates the partial subversion of a 
umver.cal affirmative by makin ? good its sub-contrary, a 
particular negative. It is maintained that no attention should 
be given to what is not practical. This may assume the logical 

£? °J a Ml VerSal ^fti^.- 1 Everything that is unp°rao 
heal should be neglected/ Desiring to Contradict this in a 
mild form, we may use the following argument — 



ARNAULD'S UNIVERSAL TEST. 173 

!No truth applicable to practice should be ) «_• 
neglected. f ™ 

Every truth applicable to practice may > . 
seem unpractical. j P 

Some seemingly unpractical truths should ) , n 
not be neglected. | tUa 

This is a syllogism in Felajpton. The major — * Some truths 
applicable to practice should not be neglected,' would equally 
suit our purpose, and with the above minor would give a 
Bokardo. In such cases as the above, it is difficult to say 
which is the grounding proposition. There is no violation of 
the essential nature of Deduction in regarding a particular 
proposition, or approximate generalization, as the ground of 
the argument. To make the reasoning a genuine deduction, it 
is required only that the grounding proposition be more 
general than the conclusion. 

Arnault? s Universal Test. 

It may be worth while to give an example of Arnauld's 
mode of testing a deductive argument without reference to its 
logical form. 

He directs the pupil simply to observe whether the conclusion 
is contained in the premises. He gives the following example 
of his method : — 

* I am in doubt whether this reasoning be good : — 

The duty of a Christian is not to praise those that commit criminal 
actions. 

Now those that engage in a duel commit a criminal action. 

Therefore it is the duty of a Christian not to praise those that 
engage in duels. 

4 Now I need not trouble myself as to the figure or mood to 
which this may be reduced. It is sufficient for me to 
consider whether the conclusion be contained in one of the two 
first propositions, and if the other show this. And I find at 
once tbat the first proposition, since it differs in nothing from 
the conclusion, except that there is in the one, those that com- 
mit criminal actions, and in the other those that engage in duels, 
— that in which there is commit criminal actions, will contain 
that in which there is engage in duels, provided that committing 
criminal actions contains engaging in duels. 

1 Now it is clear by the sense that the term those that commit 
criminal actions is taken universally, and that it extends to all 
those that commit any such actions whatever ; and thus the 



174 EXAMPLES OF THE SYLLOGISM. 

minor Those that engage in a duel commit a criminal action, 

showing that to engage in a duel is contained under this term, 

minal actions, shows also that the first proposition 

contains the conclusion.' 

This test of Arnauld's is the simplest of application to premises 
not couched in syllogistic terms. It is easily applied in any 
case : the only change of form that could aid in the scrutiny, 
would be to make the containing proposition of the same form 
with the conclusion. 

To the following arguments, the student may supply such 
grounding propositions as would give them validity : — 

A true philosopher is independent of the caprices of fortune, 
for he places his chief happiness in moral and intellectual ex- 
cellence. 

A slave is a human being, therefore he should not be held in 
bondage. 

Not being thirsty, he cannot be suffering from fever. 

The Reformation was accompanied and followed by many 
disturbances, and is therefore to be condemned. 

Solon must be considered a wise legislator, seeing that he 
athipted his laws to the temper of the Athenians. 

He was too impulsive a man not to have committed many I 
errors. 

Educated among savages, he could not be expected to know 
the customs of polite society. 

Not every advice is prudent, for many advices are not safe. 

Many assertions that are open to doubt are nevertheless 
worthy of attention, for many assertions that are open to doubt I 
may be true. j 

4 Napoleon never cared for anybody but himself." In modi- 
fied opposition to this, it may be urged that, after all, ' he ; 
was human. ' Supposing this rejoinder is intended to establish 
that Napoleon had some disinterested affections, what ground- 
ing proposition does it require ? 

In like manner, subvert the assertion, ' Napoleon never 
knew fear.' 

Volcanic eruptions, earthquakes, and plagues cannot be 
interpreted as a warning to evil-doers, for they involve alike 
the innocent and the guilty. 

Some dogs are useful animals, for is not the retriever useful ? 

All zeal is not virtuous, there being a zeal that has no dis- 
cretion. 

'TaUe-turning; (you may say,) Us a thiny I don't under- 



MISCELLANEOUS EXEKCISE& 175 

gfand. 9 Admitting tins, I ask you to construct in an affirm* 
tive form, an argument which would entitle yon, logically, yet 
not convincingly, to deny the existence of table-turning. 
(Spalding). 

Miscella neous Sy Hon ism s. 

'Suppose a man says, 'I dislike all foreigners;' find a 
premise which, with his own assertion, would entitle him to 
say also, i No foreigner deserves to be liked. 1 (Spalding). 

All cold is to be expelled by heat : this person's disorder is 
a cold ; and must therefore be expelled by heat. 

No carnivorous animals have four stomachs : all ruminants 
have four stomachs : no ruminants are carnivorous. 

Some men of inferior ability are legislators. All peers are 
legislators, and some peers are men of inferior ability. 

* No war is long popular : for every war increases taxation ; 
and the popularity of anything that touches our pockets is very 
short-lived.' (Spalding). 

He that will not learn cannot become learned. This being 
so, there are many clever young men that we cannot expect 
to become learned. 

There is some anger that is not blameworthy. "What pre- 
mise do you need for the conclusion, — ' Some passions are not 
blameworthy.' 

1 No truth is without result ; yet many truths are misunder- 
stood.' What is the conclusion ? 

Some deserve to be imitated that are nevertheless fools. 
Whoever speaks the truth deserves to be imitated. 

Humanity is a moral virtue : the study of polite letters is 
humanity ; the study of polite letters is a moral virtue. 

White is a good fellow : if, therefore, linen is white, it is a 
good fellow. 

? He that says you are an animal speaks truly : he that says 
you are a goose, says you are an animal ; he that says you are 
a goose speaks truly.' (Arnauld). 

4 You are not what I am : I am a man : therefore you are 
not a man.' (Arnauld). 

One symptom of the plague is fever; this man has fever; 
therefore he has the plague. 

Some objects of great beauty answer no other perceptible 
purpose, but to gratify the sight : many flowers have great 
beauty ; and many of them accordingly answer no other pur- 
pose but to gratify the sight. 

Every good statesman is favourable to progress. Some 



176 EXAMPLES OF THE SYLLOGISM. 

members of Parliament, not being favourable to progress, are 
iv »t good statesmen. ## # 

4 Unpleasant tilings are not always injurious; afflictions are 
often salutary.' Supply the missing premise. 

John is taller than William ; William is taller than Charles ; 
John is taller than Charles. 

4 Ol two evils the less is to be preferred ; occasional turbu- 
lence, therefore being a less evil than rigid despotism, is to be 
preferred to it.' (Whatleyj. 

All fixed stars twinkle ; yonder star twinkles ; therefore it 
is fixed. 

All that do not act foolishly are respectable ; all fools act 
foolishly ; no fools are respectable. 

4 .Most men that make a parade of honesty are dishonest ; 
this man makes a parade of honesty.' Can we conclude that 
he is dishonest ? 

Ill doers are ill dreaders. This man dreads evil, and is, 
therefore, a scoundrel. 

All aristocracies are self-willed ; some self-willed people are 
not cruel ; some aristocracies are not cruel. 

Some democracies are not persistent in their designs ; the 
Government of the United States is a democracy ; the Govern- 
ment of the United States is not persistent in its designs. 

All plants contain cellular tissue ; no animals are plants ; no 
animals contain cellular tissue. 

4 1 snatch at the conclusion that every eager desire is an 
evil thing ; since I know that the desire of evil is evil, and 
that not a few eager desires have evil objects.' (Spalding). 

A good marksman must have a steady hand ; George has a 
steady hand ; therefore, George is a good marksman. 

Flotation is possible only in liquids, and so not possible in 
this water, which is frozen. 

Poetry is not Science. The characteristics of Science are 
truth and generality, and Poetry possesses neither. 

Nothing that is not possible for man to do has ever been 
done by man. Raising the dead is not possible for man, and, 
consequently, has never been done by man. 

4 It 1 know that Messieurs A. B. and C. are not only learned, 
men but also silly ones, will you allow me to draw any infer- 
ence ?' (Spalding). 

Irrational prejudice is symptomatic of a weak mind, and we 
sometimes see it in very learned men. State this in syllogistic 
form, and draw the legitimate conclusion. 

One who misapplies riches deserves poverty ; which one who 



EXAMPLES OF CHAINS OF REASONING. 177 

is benevolent does not deserve. Is the legitimate conclusion 
consonant with fact ? 

1 If a rule never is, and a principle always is, a law admitting 
no exception, judge that a rule must be something different 
from a principle/ (Spalding). 

No branch of science can be made absolutely perfect, yet 
all branches of science are worthy of diligent culture. What 
inference do you draw from this ? 

' What was it that first gained him the public ear ? It cer 
tainly was not the pure Saxon-English in which his sentences 
are clothed, for, alas ! we find that many writers who neglect 
their grammar even, secure an immence audience, to the de- 
light of their publishers, and their own gratification/ 

* It has been supposed by some philosophers, that electricity is 
the real agent by which the nerves act upon the muscles. But 
there are many objections to such a view ; and this very im- 
portant one among the rest, — that electricity may be trans- 
mitted along a nervous trunk which has been compressed by 
a string tied tightly round it, whilst the passage of ordinary 
nervous power is as completely checked by this process as if 
the nerve had been divided.' 

The following are examples of chains of reasoning, resolvable 
into consecutive syllogisms. 

1 The concept ■ horse ' cannot, if it remain a concept, that is, 
a universal attribution, be represented in imagination ; but ex- 
cept it be represented in imagination, it cannot be applied to 
any object ; and except it be so applied, it cannot be realized 
in thought.' (Hamilton). 

1 But, to prove that moral sentiments are instinctive or 
inscrutable, it is boldly asserted, by the advocates of the 
hypothesis in question, that the moral sentiments of all men 
are precisely alike. 

f The argument, in favour of the hypothesis, which is raised 
on this hardy assertion, may be stated briefly in the following 
manner ; — -No opinion or sentiment which is a result of observa- 
tion and induction is held or felt by all mankind. Observation 
and induction, as applied to the same subject, lead different 
men to different conclusions. But the judgments which are 
passed internally upon the rectitude or pravity of actions, or 
the moral sentiments or feelings which actions excite, are 
precisely alike with all men. Consequently, our moral 
sentiments or feelings were not gotten by our induct'* ms from 



178 RECENT ADDITIONS TO THE SYLLOGISM. 

tho tendencies of the actions which excite them: nor were 
Bontiments or feelings gotten bj inductions of others, and 
1 upon onr minds by human authority and ex- 
ample. Consequently, our moral sentiments are instinctive, or 
are ultimate or inscrutable facts. 1 (Austin.) 

•The general object which all laws have, or ought to have, 

in common, is to augment the total happiness of the conimun- 

and therefore, in the first place, to exclude, as far as may 

very thing that tends to subtract from that happiness : 

in other words, to exclude mischief. But all punishment is 

lief: all punishment in itself is evil. Upon the principle 

oi* utility, if it ought at all to be admitted, it ought only to be 

admitted in as far as it promises to exclude some greater evil.' 

(Bentham). 

1 If our intellectual part is common, the reason also, in respect 
of which we are rational beings, is common: if this is so, com- 
mon also is the reason which commands us what to do, and 
what not to do ; if this is so, there is a common law also; if 
this is so, we are fellow-citizens ; if this is so, we are members 
of some political community ; if this is so, the world is in a 
manner a state.' (Marcus Antoninus). It is not to be sup- 
posed that all these transitions make distinct syllogisms ; some 
are at best but immediate or equivalent transitions. 



CHAPTER n. 
EECEXT ADDITIONS TO THE SYLLOGISM. 

Hamilton's additions. 

Sir William Hamilton's extensions of the theory and the 
forms of the syllogism are chiefly based on the Quantification 
of the Predicate, and on the full development of the two 
modes of Quantity-— Extension and Comprehension. He has 
also much criticism in detail on many parts of the syllogistic 
theory. 

It has been seen (p. 86) that the thorough quantification of the 
predicate yields four new proposition^], forms, making eight 
m all. Two of these, the affirmative forms, ' All X is all Y,' 
4 Some X is all Y,' which are held by De Morgan and by Mill, 



QUANTIFICATION OF THE PKUDICATE. 179 

to be compound propositions, have been adopted by some other 
logicians, as Thomson ( 4 Laws of Thought') and Spalding. 
The remaining two forms — the negative 4 All X is not some V,' 
'Some X is not all Y ' have been set aside as not occurring in 
actual instances. 

The addition of two new forms greatly increases tho number 
of possible syllogistic moods. By trying all the combinations 
of three propositions out of six, and by rejecting all that violato 
laws of the syllogism, and all that repeat others, Dr. Thomson 
makes out 22 moods in the First Figure, 20 moods iti tho 
Second Figure, 20 moods in the Third Figure ; so that apart 
from the Fourth Figure, of which no account is taken, there 
are 62 moods. We give, as examples, some of the new moods. 

U U U contains three universal affirmatives with universal 
predicates. 

All Y is all Z 
All X is all Y 
All X is all Z 
a syllogism, to which there is no counterpart in nature, unless 
the terms are merely different names for the same thing ; as 
'all water is all oxide of hydrogen.' We may find a proposi- 
tion whose terms are of co-equal extent to constitute a major, 
(all matter are all gravitating things) ; but we shall probably 
never be able to couple with this a minor also co-extensive in 
its terms, if these terms really mean different things. 

U E E is an example, constituting an exception to the canon 
requiring the minor in the First Figure, or normal deductive 
syllogism, to be affirmative. 

All Y is all Z All matter is all gravitating things 

No X is Y No mind is matter 

No X is Z No mind gravitates 

Here the quantification of Z (universal) avoids illicit process 
of the major. 

It is not pretended that any useful form grows out of these 
additions to the syllogistic moods ; and even as a formal 
exercise, no one has thought it worth while to state them in 
full ; far less to provide examples of them in the concrete. 

Only Hamilton himself (followed by Professor Spencer 
Baynes) has endeavoured to enumerate the syllogistic moods 
growing out of the eight quantified propositional forms. He 
even gives the number variously. The earliest statement is 
thirty-six valid moods, for each figure (excluding the Fourth), 
that is, twelve affirmative, and twenty-four negative. Dr. 
Thomson has tabulated the forms, agreeing with Hamilton so 



180 HAMILTON'S ADDITIONS OF THE SYLLOGISM. 

far, but deducting from Hamilton's complete list as useless 
though possible varieties, 14 moods in the first figure, 16 in 
thr Mc .n.l, and 1G in the third. He thus reduces Hamilton's 
moodi to 62. In a later statement Hamilton gives 42 
syllogisms, reducible to 21. 

Bhllogimns viewed either in Extension or in Comprehension. It 
is a threat point with Hamilton to show that the common syl- 
logism is defective, from not being expressed both in Extension 
and in Comprehension. He complains that all logicians, with 
the doubtful exception of Aristotle, have limited their con- 
sideration to reasoning as given in the quantity of Extension, 
He exemplifies the difference of the two syllogisms thus . — 
Extension. Comprehension. 

B is A C is B 

C is B B is A 

C is A C is A 

All men are mortal Caius is a man 

Caius is a man All men are mortal 

Caius is mortal Caius is mortal 

In the first example the class ' mortal ' contains under it 
the class man ; in the second example, the attributes of * man 9 
contain in them the attribute P mortal.' 
The following is an example in Celarent, 

Extension. Comprehension. 

No men are gods Kings are men 

All kings are men Men are not gods 

No kings are gods Kings are not gods 

The second form (Comprehension) may be read thus : — 
The attributes of a king contain the attributes of a man. 
The attributes of a man do not contain the attributes of a god. 
The attributes of a king do not contain the attributes charac- 
teristic of a god. 

It is to be remarked, with reference to this scheme of double 
syllogisms, according as the terms are taken in extent, or in 
intent—breadth or depth— that the two modes express one 
and the same meaning; and that the really fundamental 
meaning is Intent, or the Connotation of the Terms employed. 
The real meaning of the last example is, first, that the 
attributes connoted by the term, man, fail to accompany, or 
are incompatible with, the attributes connoted by the term, 
god (major) ; that the attributes connoted by ' king ' are 
accompanied with the attributes connoted by 'man/ The 
other form however, falls readiest into common language, 
the form of Extension, that is, of inclusion or exclusion of 



SYLLOGISMS IK COMPKEIIENSION. 181 

classes; men are out of the class of gods; kings are 
in the class men; therefore, kings are our. of t 
gods. This is a more concrete and intelligible form; still, it 
is not the contrast or the opposite of the other. We do Dot 
think of this form justly, correctly, unless we conceive the 
terms as determined by their connotation. The extent is 
bounded solely by the intent. It is not as if we had a com- 
plete list of men, and a complete list of kings, and saw the 
kings inserted among the men, while the list of men had 
nothing in common with the list of gods. This is the full and 
literal rendering of the reasoning in extension ; and the very 
statement of it is enough to show that we do not reason so. 
When we speak of a class, we do so in a figurative manner; 
we suppose an actual array of individuals when there is no 
such array ; there being only the defining mark, the connota- 
tion of them, to define them whenever they appear. The 
extent of * man ' is the imaginary aggregate of all objects 
agreeing in the marks connoted by the term, the defining 
characteristics of man ; if we lose sight of this condition for a 
moment, we have nothing fixed in our grasp. Accordingly, 
comprehension is inseparable from extension in every case ; it 
is an ever present fact, without our topsy-turvying the 
syllogism, or constituting a parallel array of moods to match 
the moods in extension. 

Hamilton's forms in comprehension depend solely on his in- 
troducing the idea of ' containing and contained ' into the 
groups of attributes signified by the terms of the proposition. 
A king has more attributes than a man ; the individual person 
Frederick the Second' has more attributes than a king. Thus, 
Frederick is the largest term, in point of number of attributes, 
man is the smallest. Hence we may, by straining a metaphor, 
apply the relation of whole and part, containing and contained, 
to this circumstance, as well as to the groups (in extension) 
men, kings, Frederick ; and may carry the analogy so far as 
to construct syllogisms to match. But no new or distinct 
meaning is conveyed ; and there is not even a more intelligible 
rendering of an old meaning. 

Hamilton, in discussing the conditions of the Distinctness of 
Notions, remarks justly that the highest degree of distinctness 
cannot be attained without fixing the Comprehension, in other 
words, the meaning, definition, or connotation of the term. 
(Lectures on Logic 1. 16b). He remarks also that the quantity 
of Extension is a creation of the mind itself, and only created 
through, as abstracted from, the quantity of comprehension; 



1S2 DE mokgan's additions to the syllogism. 

whereas the quantity of comprehension is at once given in the 
nature of things (p. 218). All which tends to the conclusion 
that the comprehension is what we think of in a notion ; and 
ijnently the comprehension cannot be left out of the ac- 
count in any syllogistic form. It is the power behind the 
throne, even when extension is the ostensible reigning circum- 
Mai I 

In objecting to the Fourth Figure, Hamilton grounds his 
dislike on the circumstance, that the premises proceed in the 
whole of comprehension, while the conclusion is drawn in the 
counter whole of extension. He explains the matter thus. 
The scheme of the Figure is — 
PisM 
M is S 
SisP 
Now in the premises P is contained under M ; and M con- 
tained under S ; whence in the conclusion we should expect P 
to be contained under S. In this, however, we are disappointed ; 
for the reasoning suddenly turns round in the conclusion, and 
affirms S as a part of P. [Not strictly correct ; for S is qualified 
by * some/ which may still leave it the larger term ; ' Some S 
is P.'] If we had an affirmative syllogism in the form 
All P is M All kings are men 

All M is S All men are fallible 

All S is P All fallible beings are kings 

we should have an illegitimate inference ; which might no 
doubt be evaded if the conclusion could be read thus — 

All the attributes of fallible beings are contained in the at- 
tributes of Kings. 

But no one ever reads the figure in this way. 

DE MORGAN'S ADDITIONS. 

We have seen Mr. De Morgan's views as to Terms, and his 
enumeration of Fundamental Propositions. Before proceeding 
to view his enlargements of the Syllogism, we shall advert to 
his remarks on the Copula. 

He complains that the 'is' of logicians is not confined to 
one strict meaning. It professes to be a word of the highest 
abstraction, a formal mode of joining two terms, carrying no 
meaning; and obeying no law, except such as is barely neces- 
sary to make the forms of inference hold good. ' X is Y ' com- 
imtx as to nothing specific. Yet, at times, logicians employ it 
in the sense of identity. The best description of its employ- 



COPULAR RELATIONS. 183 

ment, he considers to bo — ' agreement in some understood, and, 
for the occasion, unvarying particular.' 

He supposes that a copular symbol had been used, in 
of 'is;' the effect of which would have been to stamp upon 
the copula the character of an abstraction, as is done by the 
use of symbols, X, Y, Z, for terms. Had such a symbol been 
used, the copular conditions would have been stated. Tin 
are two in number. The first is transitiveness ; meaning that 
if X stands in a certain relation to Y, and Y in the same re- 
lation to Z, X stands in the given relation to Z. Very many 
copulas show this transitive relation ; — is, — rules, — lifts, — 
draws, — leads to, — is superior to, —is ancestor to, — is brother 
of,— joins, — depends on, — is greater than, — is equal to, — in 
less than, — agrees with (in a given particular), &c. 

The second condition is convertibility, in which the relation 
is its own correlation ; whatever X is to Y, Y is to X. In a 
certain number of the foregoing examples, there occur con- 
vertible relations; is, — is brother of, — joins (if a middle 
verb), — is equal to, — agrees with. There are cases of con- 
vertibility without the transitive character ; converses with, — 
is in the habit of meeting, — is cousin of, — is in controversy 
with, &c. 

Again, there are copula not convertible, but correlative; A 
gives to B ; B receives from A. These forms also are duly 
reasoned upon ; and syllogisms might be constructed accord- 
ingly. Every X gives to a Y ; Some Xs give to no Ys ; No 
X gives to a Y ; Every X receives from a Y ; Some Xs receive 
from no Ys, — are examples of the propositional forms. They 
are all capable of conversion, by substituting the correlative 
copula. 

The admission of Relation in general, Mr. De Morgan con- 
tends, and of the composition of relation, makes logic more 
in alliance with ordinary thinking. The reduction of all 
relations by ' is ' — * mind acts on matter, mind is a thing 
acting on matter,' — is a systematic evasion, hostile to the pro- 
gress of the science. 

Logicians are aware that the form ' A equals B, B equals C, 
therefore A equals C ' is not reducible to the syllogism. So 
with the relation of ' greater than/ in the argument a fortiori 
Yet, to the ordinary mind, these inferences are as natural, as 
forcible, and as prompt, as the syllogistic inference. Mr. De 
Morgan, therefore, would propose to include all such forms in 
one sweep by a generalized copula of relation, which would be 
formally embodied and symbolized in propositions. Thus — 
9 

f 



184 DE morgan's additions to the syllogism. 

Every X Las a relation to some Y 
Every Y has a relation to some Z 
from which the inference would be that * Every X has a com- 
pound relation to some Z ;' the compound of the relations X 
to Y and Y to Z- Under this form, we reason, John can 
control Thomas ; Thomas can control William ; John can 
control William. Under the general and comprehensive 
copular relation, specific modes might be developed for specific 
purposes. The Logical copula in common use is the equival- 
ent of ■ fastened to/ ' connected with,' « co-exists with/ and 
nuiy be considered for logical purposes the most important 
The copula of equality and inequality is developed in Mathe- 
matics, and an inference according to it would probably be 
culled a mathematical inference. 

The converse copular relation, * causes,' would be singled 
out on account of its great importance: — A causes B, B is 
erased by A. We practically construct syllogisms from these 
propositions, without passing through our minds the formal 
transformation to — A is the cause of C. 

These remarks of Mr. De Morgan's are undoubtedly just 
and cogent; and they are highly valuable in the way of eman- 
cipating the student from the Aristotelian limits, as well as 
for pointing out the vagueness and vacillation of the ordinary 
copula. Still, we could hardly afford the labour of following 
out the technical developments of half-a-dozen distinct forms 
of copula. It is well to see that such developments are not 
merely competent in themselves, but needed to formulate the 
whole compass of our habitual thinking and reasoning. Being, 
however, aware of this fact, we must be content with con- 
structing one scheme adapted to the most useful and most 
frequently recurring relationship ; which scheme we should 
then regard as an example of the rest, one out of many. Any 
one having Mr. De Morgan's genius for the construction of 
forms might do well to develop a variety of copular relations; 
iVoin these such selections might be made as would extend 
the inferential grasp of the ordinary student. 

Mr. De Morgan's Extensions of the Syllogistic forms are 
avowedly based upon the full recognition of contraries, as laid 
out in his scheme of eight fundamental propositions. Also, 
by providing symbols for contraries he can exhibit all denials 
as assertions ; No X is Y, is All X is r (U— Y). Hence, the 
unit syllogism may be represented in an affirmative form—* If 
an X be a Y, if that same Y be a Z, then the X is a Z.' 



SYLLOGISTIC FORMS. 185 

All syllogisms are derivable from the following combinations 
of Premises : — 

(1) All Xs are Ys, and all Ys are Zs. Tin conclusion is 
AUXsareZ^; the unit syllogism. This is the inversion of 
the Aristotelian order of premises, but it is in the author's 
view the proper and the natural order. 

(2) Some Xs are Ys, all Ys are Zs ; some Xs are Zs. The 
unit syllogism is here, as it were, cut down to tho form, — ' as 
often as there are Xs in the first premise, there are in the con- 
clusion/ 

(3) Some Xs are all Ys, some Ys are Zs ; conclusion — some 
Xs are Zs. In point of form, this is the previous case inverted. 
The universal middle term (all Ys) is transferred from the 
second premise to the first. 

(4) Some Xs are all Ys, All Ys are Zs ; Some Xs are Zs. 
Here, although there is an additional universal middle, all 
Ys, occurring in both premises, there is no stronger conclusion 
than in the two preceding cases, where the middle term is 
universal (or distributed) only once. 

These are all the possible couples of affirmative premises 
apart from any cognisance of contrary terms. Now, all 
negations may be rendered as affirmations about contraries ; 
and therefore the application of these cases to all combinations 
of propositions, direct or contrary, will give all possible valid 
syllogisms. 

Taking X, Y, Z, and their contraries x, y, z, there are eight 
combinations of threes : — X Y Z, x Y Z, x y Z, x y z, X Y z, 
Xy Z, X y z, x Y z. To each of these the four modes of inference 
can be applied ; and when x, y, z, are read as the contraries of 
X, Y, Z, we obtain the proper expression of the syllogism. 
Thus, the first or unit syllogism, applied to x y Z, gives Every 
x is y, Every y is Z ; therefore, Every x is Z. This unfolded, 
by giving the equivalents of the contrary terms x, y, in the 
ferms X, Y, the whole syllogism may be read thus : — 

Every x is y (All not-X is not-Y) is the same as No Y is 
not X, or Every Y is X, or Some Xs are all Ys. 

Every y is Z (Every not-Y is Z) is the same as Everything 
is either Y or Z (one of De Morgan's new propositi onal forms). 

In like manner, the conclusion Every x is Z, (Every not-X 
is Z) is Everything is either X or Z. The syllogism then is : — 
Some Xs are all Ys (Every Y is X). 
Everything is either Y or Z. 
Everything is either X or Z. 

A syllogism not in the Aristotelian figures. From the very 



186 DE mobgah's additions to the syllogism. 

wide compass of the form, Everything is either Y or Z, there 
can bQ few applications of such a syllogism. 

Some extended things are all material things. 
I\ery thing is either material or pertaining to mind. 
Everything is either extended or pertaining to mind. 

The remaining seven forms being expressed and unfolded in 
like manner, there would arise the eight forms of universal 
syllogism, that is universal premises with universal conclu- 
sion. 

Again, apply case second to the same eight forms — Some 
X> ate Ys, all Ys are Zs ; some Xs are Zs ; and there emerge 
eight minor-particular syllogisms, particular conclusion with the 
minor (or first) premise particular. 

Apply case third— Some Xs are all Ys, some Ys are Zs ; 
some Xs are Zs — and we have eight major-particular syllogisms, 
particular conclusion with the major (or second) premise par- 
ticular. 

Apply case fourth— Some Xs are all Ys, All Ys are Zs, 
Some Xs are Zs — and we have eight strengthened particular 
syllogisms, universal premises with particular conclusion By a 
strengthened syllogism, the author means one whose premises 
are stronger than they need be to bear out the conclusion. 

The above 32 forms are those that give inference, out of 64 
possible combinations of the premises. The remaining 32 
forms could be drawn out by representing the eight proposi- 
tional arrangements, X Y Z, x Y Z, &c, in four varieties of 
premises, which the author states. Thus : (1) Some Xs are 
some Ys, Some Xs are all Ys; (2) All Xs are some Ys, Some 
Xs are some Ys ; (3) Some Xs are some Ys, Some things are 
neither Xs nor Ys ; (4) Some Xs are Ys ; All Xs are not some 
Ys. From none of these combinations of premises could any 
inference be drawn. 

The test of validity, and the rule of inference, the author 
expresses thus : — 

There is inference (1) When both the premises are uni- 
versal. (2) When, one premise only being particular, the 
middle term has different quantities in the two premises. 
Either of these cases happening, the conclusion is found by 

tfing the middle term and its quantities. Premises of like 
quality give an affirmative conclusion; of different quality, a 
negative. A universal conclusion follows only from universals 
with the middle term differently quantified in the two. From 
two particular premises nothing follows. 

A particular premise having the concluding term strengthened 

\ 



RULES OF INFERENCE. 187 

(that is, made universal), the conclusion is also strengthen id 
and the syllogism becomes universal ; for example, Darii % by 
this process, would become Barbara. With the middle term 
strengthened, the conclusion is not strengthened, and there 
being, therefore, a surplus of affirmation in the premises, the 
syllogism forms what the author calls a strengthened particular 
syllogism. Thus, Darapti, in the third figure — 

All Y is Z 

All Y is X 

Some X is Z — ■ 
has the middle term universal in both premises, when once is 
enough , there would be inference with ' Some Y is X ' in the 
minor. Felapton and Fesapo are other examples. 

A different case is exemplified in Bramantip. The two 
universals — * All Z is Y, All Y is X,' yield the universal 'all 
Z is X,' which, for the sake of a different order of the terms 
in the conclusion, is converted and weakened into the particular 
' Some X is Z.' This is termed by the author a weakened 
universal. 

Each form of proposition has corresponding to it certain 
opponent forms. Thus, if the propositions A, B, gives C, they 
cannot give C (the contrary of C). Hence A and c being true, 
B is false or B true ; that is A, c, give B ; that is to say, either 
premise joined with the contrary of the conclusion gives the con- 
trary of the other premise. Thus, there are two opponent forms 
to every syllogism. And the syllogisms may be so grouped in 
threes, that each one of any three may have the two others 
for opponents. Barbara has, for opponent forms, Barolco and 
Bolcardo. 

Mr. De Morgan considers it of importance to remark that 
the adjective for expressing universal quantity — .' All' means 
two things, which should be kept distinct. It may be * All ' 
collectively, the entire collection or aggregate of individuals; 
this he calls the cumular form ; and it may be 'all ' distribu- 
tively, iu the sense of 'every one/ or 'any one,' however 
taken, which he calls the exemplar mode. He holds that the 
language of Aristotle, and of his immediate followers, was 
exemplar and not cumular; irus uiCpivwo^ he contends, is each 
or every man, not all man. ' All man/ as a comprehensive 
genus, has parts, — for example, the several species or varieties 
of men ; ' every man ' has no parts, but makes assertions about 
every individual of the genus man. 

The exemplar mode is that used in geometrical proof. A 
proposition in Euclid assumes some one case, and the demon- 



IS8 DE MORGAN'S ADDITIONS TO THE SYLLOGISM. 

utration is such that nothing prevents the one chosen from 
me. It would be useful in geometry, to admit the 
form 4 any one X is any one Y.' 

In negation, the exemplar form is needed. ' All men are 
does not deny the proposition, 'All men are fishes.' 
The denial would, however, be given in 'Every man is not 
any fish.'* 

Properly speaking, the cumular proposition can be found 
proved only through exemplars; hence the exemplar precedes 
in the order of thought ; a circumstance justifying its adoption 
as the basis of a logical system. According to it, quantity is 
mode of selection by example; universal is replaced by wholly 

i 'finite; particular by not wholly indefinite. The forms of 
the propositions would be modified thus : — ■ 

Any one X is any one Y. X and Y singular and identical. 

Suine one X is not some one Y. Either X not singular, or 
Y not singular ; or if both singular, not identical. 

Any one X is some one Y. All Xs are some Ys. 

Some one X is not any one Y. Some Xs are not (all) Ys, 

Some one X is any one Y. Some Xs are all Ys. 

Any one X is not some one Y. All Xs are not some Ys. 

Any one X is not any one Y. All Xs are not (all) Ys. 

Some one X is not some one Y. Some Xs are some Ys. 

The * Numerically Definite Syllogism ' is a scheme of infer- 
ence which supposes exact numbers to be given. 

If in 100 instances of any thing, 70 are Xs, and 30, Ys, 
then at least 20 Xs must be Ys. The author develops at great 
length a symbolical scheme founded on this assumption. 

Syllogisms with numerically definite quantitv occur rarely, 
if ever, in common thought. But it is not unfrequent to find 
iorms where the number of instances of one term is the whole 
number of instances of the other term ;— ' For every Z there 

/ 1 M V*ii 11, . in a controversi al nx)te to his chapter on the Functions 
or the Syllogism, makes the following remark:— The language of 
iMtmcmatmn would, I think, be brought into closer agreement with 
m\ nature of the process, if the general oppositions employed 
m reasoning instead of being in the form All men are mortal, or 
Every man is mortal, were expressed in the form Am; man is mortal. 
I mode of expression exhibiting as the tvpe of all reasoning from 
entice •• The men A. B, C, &c. are so and so, therefore any man is so 
and so, would much better manifest the true idea- that inductive reason- 
ing is ^uwavs at the bottom, inference from particulars to particulars, and 
KttttS^ inreasonm^isto vouch 



THE ARISTOTELIAN SYSTEM COMPARED. 189 

is an X that is Y; some Zs are not Ys ;' ' For every mat) in 
the house there is a person that is aged ; some of the men arc 
not aged ;' from which it follows, but not by any common form 
of syllogism, that 'some persons in the house are not men.' 

To this case the author applies the designation 'syllogism 
of transposed quantity.' Of terms in common use the only 
one that gives syllogisms of this character is ' most :' — ' Meat 
Ys are Xs ; most Ys are Zs ; therefore some Xs are Zs.' 

Adverting to the distinction of Figure, he styles the First 
the figure of direct transition ; the Fourth, which is nothing 
but the first with a converted conclusion, the figure of inverted 
transition; the Second, the figure of reference to (the middle 
term) ; the Third, the figure of reference form (the middle 
term). Apart from the conversion of the conclusion, the 
Fourth Figure is the most natural order, as it takes up what 
was left off with — ' X is in Y, Y is in Z, therefore X is in Z :' this 
is the first figure, according to the simplest arrangement of 
the premises. 

In the author's system, however, Figure attains importance 
only through a wider view of the copular relation. 

Mr. De Morgan compares his system with the Aristotelian, 
of which he regards it as an extension, through the single de- 
vice of adding contraries to the matters of predication. (Hamil- 
ton also claims to extend Aristotle, but on a different principle). 
Accordingly the Aristotelian syllogisms may be all collected 
from the preceding system, by the following modifications. 
1. The exclusion of all idea of a limited universe, of contrary 
names, and of the propositions, ' Every thing is either X or Y,' 
' Some things are neither Xs nor Ys.' 2. The exclusion of the 
form of conversion, ' Some Xs are all Ys.' 3. The exclusion of 
every copula except the transitive and convertible copula. 4. 
The regarding of the identical pairs — No X is Y, No Y is X, 
and Some X is Y, Some Y is X — as distinct propositions of 
themselves determining distinction of figure and mood ; as 
Celarent and Cesare, Ferio and Ferison, &c. 5. The introduc- 
ing of the distinction of figure. 6. The writing of the major 
and minor propositions first and second, instead of second and 
first. 

Farther, in the Aristotelian scheme, there are four funda- 
mental syllogisms in the first figure, each of which has an 
opponent in the second, and an opponent in the third. The 
opponents of Barbara are Barolco and Bolcardo. There are 
three fundamental syllogisms in the fourth figure (Dimaris, 



190 BOOLE'S ADDITIONS TO THE SYLLOGISM. 

nes, Freshon), each of which has the two others for op* 

Altogether there are fifteen fundamental syllogisms. 

remaining four are— three strengthened particular syllo- 

ti (III), Felapton (III), Fesapo (IV), and one 

Weakened universal; Bramantip (IV). 

The Aristotelian rule that the middle term must be distri- 
buted once fails with the introduction of contraries. The rule 
to be substituted is — All pairs of universals are conclusive, 
but a universal and a particular require that the middle term 
should also be a universal and a particular, — universal in one 
premise and particular in the other. 

The rule that when both premises are negative, there is no 
syllogism, also fails. In the system completed by contraries, 
there are eight such syllogisms ; as many, in fact, as with pre- 
mises both affirmative. But in these cases, as before re- 
marked, the premises are not both negative in reality. 

Again, on the rule ' that two particular premises can give 
no conclusion,' the author brings forward as a legitimate 
inference, 4 Most Ts are Xs, most Ts are Zs, therefore some 
Xs are Zs ; most men wear coats, most men wear waistcoats, 
therefore some men wear both coats and waistcoats/ He 
develops this form at length into a symbolical scheme, under 
the naue of * The numerically definite syllogism/ 

Mr. De Morgan's system, on the whole, is characterized by 
an immense multiplication, not only of symbolical forms, but 
of verbal designations for the relationships growing out of the 
syllogism. 

boole's additions. 

The late Professor Boole, of Cork, published two works 
on Formal Logic The first and smaller, entitled — 'The 
Mathematical Analysis of Logic,' comprised an Algebraic 
rendering of the syllogism, showing how all the moods might 
be symbolically deduced. The second and larger work, en- 
titled— 4 An Investigation of the Laws of Thought, on which 
are founded the Mathematical Theories of Logic and Proba- 
bilities,' takes a much wider sweep, and is an entirely new 
application of the symbolical methods of Algebra, to Inference, 
both Immediate and Mediate; the largest share of attention 
being given to the first, or the so-called Immediate Inference, 
r l lie author also extends the same nomenclature and handling 
to Probabilities. 

Besides the novel employment of symbolical processes of the 
Aljpbi&ic kind, the work is intended to bear fruit in other 



CONNEXION OF LOOIC AND MATHEMATICS. 191 

ways, la using the title ' Laws of Thought,' tho author in- 
dicates that one purpose of his theory of Reasoning is to throw 
light upon the workings of the Intellect. He considers that 
our views of the Science of Logic must materially influence, 
perhaps mainly determine, our opinions upou the nature of the 
intellectual faculties. For example, whether reasoning con- 
sists merely in the application of certain first or necessary 
truths, originally imprinted on the mind, whether the mind is 
itself a seat of law [whatever that may mean], or whether all 
reasoning is of particulars, concerns not Logic merely, but also 
the theory of the intellectual faculties. It cannot be said, how- 
ever, that the author has been able to decide which alternative 
is the correct one. 

He farther proposes to elucidate the subtle connexion be- 
tween Logic and Mathematics ; how far a common theory is 
applicable to both kinds of reasoning, and how far the likeness 
fails. He holds that the ultimate laws of Logic are mathe- 
matical in their form, that they are, except in a single point, 
identical with the general laws of Number. The exhibition 
of Logic in the form of a Calculus is not arbitrary : the ultimate 
laws of thought render that mode possible, and forbid the 
perfect manifestation of the science in any other form. It is 
not of the essence of Mathematics to be conversant with the 
ideas of number and quantity. The author does not design to 
supersede, by symbolic processes, the common forms of reason- 
ing ; nevertheless, cases may arise where the value of scientific 
procedure, even in things confessedly within the scope of 
ordinary reasoning, may be felt aud acknowledged. 

The author's scheme starts with the consideration of Lan- 
guage as an instrument, not of communication merely, but of 
Reasoning ; it being his intention to substitute, for ordinary 
language, a set of symbols adapted to perform this function in 
a more effective manner. 

The signs composing Language, with a view to Reasoning 
especially, are characterized in the following definition : — ' A 
sign is an arbitrary mark, having a fixed interpretation, and 
susceptible of combination with other signs in subjection to 
fixed laws dependent upon their mutual interpretation.' Tho 
first part is obvious ; a sign, in its primary invention is purely 
arbitrary ; ' house ' and ' domus ' are equally good for the 
purposes of language. It is also obvious that each sign should 
possess a fixed interpretation, that there should never be any 
ambiguity of meaning. Ordinary language is greatly liable to 



192 BOOLE'S ADDITIONS TO THE SYLLOGISM. 

this infirmity; hence, one of its defects as an instrument of 
Lastly, signs mnst be susceptible of combination 
with other siuns, wliich combinations must have fixed laws 
depending upon their mutual interpretation. 

Tie author proceeds to explain his artificial symbols for 
superseding, by a higher mechanism, the vocables of our ordi- 
nary speech. The symbols, and their connecting signs of 
operation, are borrowed from Algebra, and are manipulated by 
the algebraic processes, after allowances are made for the 
difference between the material of Logic, and the material of I 
Mathematics (Number and Quantity). 

All the operations of Language, as an instrument of Reason- 
ing, may be conducted by a system of signs composed of the 
following elements: — 

First, L'teral symbols, as x, y, z, &c, representing things as 
sul jects of our conceptions. For the object ' man' we may use 
x, for a ' biute,' ?/, for the quality ' living/ L and so on. 

Second, feigns of operation, as +, — , X, standing for the 
operations whereby conceptions are combined, or, when com- 
bined are resolved into their elements ; l men and brutes' may 
1 e represented by x -f y. 

Third. The sign of identity =. 

These symbols of Logic are used according to definite laws, 
partly agreeing with, and partly differing from, the laws of 
the corresponding symbols in the science of Algebra. 

The first class of symbols above given are the appellative or 
descriptive signs, expressing either concrete things, or the 
qualities of things ; that is to say, they are the equivalents of 
the two appellative parts of speech, the Noun and the Adjec- 
tive. Thus, let x denote 'men/ or all men ; and let y denote 
the adjective good ; then all good men would be expressed by 
m me suitable combination of x and y. Now the suitable com- 
bi nation, for the case of a thing qualified by an attribute, or of 
two cr more > co-inhering attributes is a product x X y, or 

y. VV by this, and not the sum x + y, is the proper symbol, 
the auther does not specifically explain ; the means, as in 
other symbolical sciences, are left to be justified by the end, 
namely arriving at true results. So if x stands for * white ' 
or white things y for sheep, xy stands for < white sheep > 
ana it z stands for * horned/ z x y will represent 'horned 
wnue sheep. In this symbolism, the order of the symbols is 
unimportant, jnst as the order of the adjective and the sub- 
Mantive is indifferent as regards the meaning; « good man,' 

vir bonus are equally accepted by the mind to suggest that 

V 



x 



SYMBOLS FOR PARTS AND WHOLE. i<J3 

the conception 'man' is to be limited by the conception 
* good.' Hence we may nse at pleasure x ?/, and y x ; x y x f 
and z y x, &c. 

It is a law of speech that an appellative gains nothing (ex- 
cept perhaps rhetorically) by repetition or duplication ; 4 good, 
good,' is the same as good ; ' horse, horse,' is the same as horse. 
To adapt this to symbols, x x would amount to no more than 
x ; that is, using = (as in Algebra) for equivalence, or iden- 
tity, x x — x. Here Logic and Algebra are at variance, and 
the methods of manipulating logical symbols must vary ac- 
cordingly. The author shows that the form x x ^ x> or x 2 z=z 
«, has still deeper meanings. 

Next as to signs for collecting parts into a whole (quantity in 
extension) or for separating a whole into parts. These cor- 
respond to the conjunctions ' and,' ' or,' in common speech — 
' trees and minerals ; ' 4 barren mountains, or fertile vales.' 
The sign of addition is now used 5 let x be f trees ' and y 
4 minerals ; ' the conjoined expression is x -4- y. This employ- 
ment of the sign is so closely allied to addition in arithmetic, 
that it may be worked upon the same principle. Again, let 
x stand for men, y for women, and z for European ; then 
'European men and (European) women' would be represented 
by z (x + y) — z x + z y. 

Addition implies subtraction. ' All men except Europeans ' 
will be expressed by x — y. ' White men except white Asiatics ' 
(x men, y Asiatics, z white), 

2 (z — y) = zx — zy 

With a view to Propositions, it is necessary to consider the 
rendering of the copula. For this purpose all propositions have 
to be reduced to the form ' is ' or ' are ; ' ' Caesar conquered the 
Gauls,' must be resolved into ' Caesar is he that conquered the 
Gauls.' This is the copula of identity, the most generalized 
form of relationship of subject and predicate. It may be ex- 
pressed by the symbol = ; and the meaning so far coincides 
with the Algebraic meaning, that the Logical equation is little 
different from the Algebraic equation. 

Take the Proposition, ' The stars are the suns and the 
planets.' Let stars be represented by x, suns, by y, and 
planets, by z ; then, 
x = y + « 

Whence we can deduce, 

x — y — z (The stars, except the suns, are planets), 

or, x — z = y (The stars, except the planets, are suns). 

Thus, in the Logical equation, we may apply the mathe- 



194 BOOLE'S ADDITIONS TO THE SYLLOGISM. 

matical axioms 'equals added to equals give equal sums;' 
4 equals taken from equals give equal differences.' 

If two classes of things, x and y, be identical, that is, ii 
all members of the one are members of the other, then such 
members of the one class as possess a given property, z, will 
be identical with the members of the other that possess the 
Fame property. Hence, if we have the equation 

x = y: 
then, whatever class or property z may represent, we have also 
z x = z y. 

In point of form, this coincides with the algebraic law — if 
both members of an equation be multiplied by the same 
quantity, the products are equal. 

The analogy, however, does not extend to division. For, 
supposing the members of a class x, possessing the property 
z, are identical with the members of a class y, possessing the 
same propeity, it does not follow that the members of the class 
x universally are identical with the members of the class y. 
Hence, it cannot be inferred from the equation 

zx = zy, 
that the equation 

x — y. 

is also true. Thus, the process of division, as applied to 
equations in Algebra, has no formal equivalent in Logic. 
Multiplication sufficiently represents the combination or com- 
position of conceptions, but division does not appear to repre- 
sent their decomposition or abstraction. The want of analogy 
on this point, however, is not total. Even in Algebra, the 
rule of division does not hold throughout ; for example, it does 
not apply when the divisor is z = 0. Through this one 
loophole, the author is able to restore the consistency of the 
algebraical and the logical processes. 
Reverting to the equation 

he remarks that only two values of * will comply with it ; 
namely, and 1. For 2 = 0, and P = 1 ; and of no other 
numbers is the relation true. Hence, in an Algebra, whose 
symbols x, y z, Ac, never knew any values but and 1, the 
laws of operation would coincide with the laws of operation in 
liOgic. lhe two sciences are divided by no other difference 
than the manner of interpretation. 

«vmbottTo IIL, ?° ^ pr ° feSSes t0 d ™ th * ] ™* ^ the 
•jmbols of Logic, above assumed, from the laws of the opera- 



SYMBOLS FOE COMPLEX SUBJFX'TS. 193 

tion of the mind. He proceeds thus: — In every discou 
there is a limit to tho subjects considered; in other frorda, 
a universe. [He is here at one with De Morgan], Thus the 
term • men ' is used with reference to a certain implied ex: 
sion, on the part of the speaker ; it may be all men whatsoever ; 
or it may be a more limited universe, as civilized men, men in 
the vigour of life, and so on. The term ■ men ' raises in the 
mind of the hearer the beings so intended to be comprised. 
Let us next consider the employment of an adjective in addition. 
Suppose ' men ' to be spoken of in the widest sense, the uni- 
verse 'all men ; ' then the application of the adjective ' good ' 
prescribes the operation of selecting from the universe all 
objects possessing the further quality ' good ; • such selection 
corresponds to the combination — good men. Thus, the office of 
an adjective is not to add the quality, ' good ' for instance, to 
all the universe, men, but to select, from the universe, individuals 
according to the idea prescribed in the word. The intellectual 
faculties employed in these successive operations may be sup- 
posed to be those denominated Conception or Imagination, and 
Attention ; or perhaps the entire act may be summed up in 
one function of Conception. Each step in the process may be 
characterized as a definite act of conception. 

Now, the syllogism above adopted exactly corresponds to 
this operation. The symbol x directs attention upon a certain 
universe, men for example ; the symbol y, good or white, di- 
rects us to search that universe for individuals owning the pro- 
perty named ; and the combination y x, or x y y expresses the 
selection — good men or white men. This symbol will not fall 
under the relations expressed by a sum ; its meaning is a group 
qualified by the conjoined conceptions x and y, not an aggregate 
made up by adding the universe x to the universe y. In this 
way does Boole consider that he has established his positions : ( 1 ) 
that the operations of the mind are subject to general laws, and 
(2) that these laws are mathematical in their form ; whence 
the laws of the symbols of Logic are deducible from the opera- 
tions of the mind in reasoning. 

He then proceeds to determine the logical value and signifi- 
cance of the symbols and 1, to which quantities Alirebra has 
to be cut down, in order to become Formal Logic. The sym- 
bol corresponds to Nothing ; the symbol 1 corresponds to 
the universe of discourse. Nothing and Universe are the two 
limits of extension — none and all. Whatever the class y may 
be, the individuals common to it and to the class 0, or Nothing, 
are Nothing or none. That is, 

x y^= 0, or y = 



196 BOOLE'S ADDITIONS TO THE SYLLOGISM. 

Again, the symbol 1, satisfies the law of equation, 
1 X y = y, or 1 y = y 
whatever y may represent. The class represented by 1, there- 
fore must be * the Universe/ the only class containing all the 
individuals that exist in any class. 

Now as to contraries. If x represent any class of objects, 
1 — x will represent the contrary, or supplementary class, what 
remains when x is withdrawn from the Universe of discourse 
1. It* x be ' men ■ in the universe * animals/ 1 — x is the not- 
men, the remaining members, or the brutes. This coincides 
with Ue Morgan's symbolism, U — x for the contrary of a?. 

The author next offers from his fundamental logical equa- 
tion, x 2 = x, or x — x 2 = 0, a formal proof of the Law of Con- 
tiadiction, thus: — The equation admits of the form 

x(l— x) = 
which, being interpreted according to the meaning of the 
symbols, is that a class determined at once by x, and by its 
contrary 1 — x, is the same as or Nothing ; that is, does not 
exist. 

Advancing farther into the consideration of Propositions 
(chap. IV.), the author divides these into 'primary' or 
simple, and 'secondary* or complex; the one relating to 
things, the other to propositions. Under the last named class 
are included hypotheticals, &c. He begins by propounding a 
general method for expressing any 'term ' that may enter 
into a primary proposition. The method is merely the appli- 
cation of his symbols as already explained. Thus, let x repre- 
sent opaque substances, y polished substances, z stones ; then 
x y z = opaque polished jtones. 

Now as 1 — 2 represents substances that are the contrary of 
stones, or are not stones, 

x y (1 — z ) = opaque polished substances that are not stones ; 
So 

x (I — y) (1— 2 ) = opaque substances, not polished, and 
not stones. 

Again, for the case of collections of things, — or objects con- 
joined by 'and/ ' or/— the sign of addition must be added, as 
above explained. The sign ' or ' gives a disjunctive form ; all 
xsare either t/'s or z's ; and this has two meanings not dis- 
criminated by the use of 4 or/ but differently rendered in the 
formula. It is a question whether x may, or may not he both 
y and z. ' He is either a rogue or fool ; ' he may or may not 
be both, so far as this expression goes, although the more 









COMFLEX TEEMS. I97 



usual rendering would be * not both.' The two ways of sym- 
bolic expression are the following. (1) Things that are either 
ar's or f/'s, are things that if »'s are not //'s, and if i/s are not 
sc's ; that is 

* C 1 —v) + 2/(1 — »). 

(2) Things that are either aj's, or if not aj's, then ?/'s. 

x + y (l — x). 
This admits the supposition of being both x and y, a suppo- 
sition more explicitly given in the enlarged equivalent form. 

xy -\-x (I — y) + y (1— z\ 
where we have all three alternatives : x y expressing the concur. 
rence of both x and y. If he is not a rogue he is a fool, x 
fool, y rogue, a? (1 — y) ; if he is not a fool he is a rogue, 
y (1 — a;) ; he is a fool and a rogue together, a* y. 

To take a more complex example, exhibiting the full power 
of the method ; let 

x = hard, y = elastic, z = metals ; 
and we shall have the following results : 

non-elastic metals = z (I — y). 
Elastic substances, together with non-elastic metals, y + z 

(1-2/). 

Hard substances except metals, x — z. 

Metallic substances, except those neither hard nor elastic, 

z-z (1_«) (1 _ y ) orzj 1 - (1 — x) (1 - y). 

To take a still more complicated examples: ' Hard substance, 
except such (hard substances) as are metallic and non-elastic, 
and such (hard substances) as are elastic and non-metal lie/ 
Hard substances being represented by x ; substances hard, 
metallic, and non-elastic, are x z (1 — y) ; substances hard, 
elastic, and non-metallic, are x y (1 — z), and the whole expres- 
sion is 

x — iz(l — y) +xy (1 — z) > or x — x z(\ — y) — xy(l — z). 

Such is the expression of Terms. To form Propositions, 
the sign = is used for the copula of identity. Thus, to ex- 
press identity between ' Fixed Stars' and * Suns,' or to express 
that 'All fixed stars are suns,' and 'All suns are fixed stars/ 
[Hamilton's universal with universal predicate], 

x=.y. 

This is the form applicable to the verbal proposition or de- 
finition ; and the author exemplifies it by such. For example, 
Senior's definition of wealth, as consisting in things trans- 
ferable, limited in supply, and either productive of pleasure 

f 



198 BOOLE'S ADDITIONS TO THE SYLLOGISM. 

or preventive of pain, is symbolized thus. Let w = wealth; 
t = things transferable ; s ^ limited in supply ; p = pro- 
ductive of pleasure; r = preventive of pain. Now it is to be 
remarked that the conjunction 'and' is not necessary and 
might be misleading; 'and' conjoining two adjectives 'great 
and good men,' is very different from ' and ' coupling two 
groups * great men and good men;' the first is x y z, the 
Beeond x % + y z. We farther remark that the disjunctive 
4 or' in ' productive of pleasure or preventive of pain/ means 
things that * if not productive of pleasure are preventive of 
pain ;' and that, ' if not preventive of pain are productive of 
pleasure ;' and does not suppose any class of things to be both 
at once. With these explanations, the definition is embodied 
in the formula, 

w = st < p (1 — r) + r (1 — p) > 

Passing now to Real Propositions, as — * men are mortal/ we 
need a mode of rendering particular terms ; * All men are 
some mortal beings.' Let v represent an indefinite class, some 
of whose members are mortal beings ; and let x stand for the 
the entire class 4 mortal beings ;' then v x will represent l some i 
mortal beings.' Hence if y stand for men, the equation sought 
is — 

y = vx 
The qualifying symbol v is thus the mark of particularity in 
every case. In the proposition, 4 the planets are either primary 
or secondary ' (some primary bodies or else some secondary 
bodies), 

Let x represent planets (the subject) ; 
y = . primary bodies ; 
z = secondary bodies ; 
then, assuming that the planets cannot be both primary and 
secondary, the equation of the proposition is 

* = »{</ (l-*)+*(l-2/).j- 

A more simple form, stating the same proposition, is 
x = v (y + z). 

For, the meaning obviously is, that the planets fall exhaust- 
ively under the two heads, primary and secondary ; that is, are 
made up of some primary and some secondary bodies. 

buch is the symbolism applicable to affirmative real proposi- 
tions, where the predicate, as a rule, must be supposed to 
surpass the subject. The author next shows how-to express 
negative propositions. 



EXPRESSION OF PROPOSITIONS. 199 

Suppose the case, * No men are perfect beings,' a universal 
negative. Here, we make an assertion to the effect that '</// 
weu'are 'not perfect beings.' The meaning may then be 
expressed thus: — All men (subject) are (copula) not any part 
of perfect (predicate). Let y represent ' men/ and x 4 perfect 
beings.' • Not perfect beings ' are represented by the negative 
form \—x; and ' some not perfect beings/ by this form, quali- 
fied by the sign of particularity, v. Hence, the equation is 
y = v (1 — x). 

Thus, to express the form No xs are ys, we have to convert it 
into ' All xs are not (any part of) ys.' 

A particular negative proposition, 'some men are not wise,' 
is resolvable into ' some men ' (subject) ' are ' (copula) ' not 
wise ' (predicate). Putting, then, y for ' men/ x for fc wise/ 
and v for an indefinite containing some individuals of the class 
qualified t>y it, we have for 'some men/ v y, for 'not any 
part of the wise/ v (1 — x), or the equation 
v y = v (1 — x). 

So mnch for the symbolical expression of primary or simple 
propositions. It is next to be seen how these forms are turned 
to account in furnishing immediate inferences, or in exhaust- 
ing all the equivalent propositional forms of each ; in which 
operation the author principally expends the force of his 
method. 

With this view, permission must be given to work the several 
equations after the algebraical model, with the restrictions 
already stated. The reader must be satisfied from the ex- 
planations afforded that the signs used have the same force in 
Logic as in Algebra. The conditions of valid reasoning are 
then those three : — First, that a fixed interpretation be as- 
signed to the symbols ; secondly, that the formal processes of 
solution or demonstration be conducted in obedience to the 
laws laid down as to the meanings of the signs of operation ; 
thirdly, that the final result be interpreted in the same way as 
the original data. Having once clothed the logical meaning 
in the algebraic dress, the author claims to proceed exactly as 
if he had to deal with an algebraic equation wherein the symbols 
have only the two meanings and 1. 

The exhaustive renderings of each proposition are to be 
gained by a process of ' development,' which is explained at 
length, and is strictly after the manner of Algebra, with the 
conditions of value specified. The skeleton of the form of 
development is furnished from these considerations : — Suppose 
we are considering a class of things with reference to the point 



A 



200 BOOLE'S ADDITIONS TO THE SYLLOGISM. 

whether its members possess or do not possess a property x ; 
ns animals, with reference to humanity. Suppose next that 
t\m members possessing the property #, possess also a property 
u ; and that the members not possessing the property x are 
subject to a condition v. On these suppositions the class in its 
totality is represented by 

u x -f- v (1 — x). 
Any function of x, f (x), wherein # is a logical symbol, 
susceptible only of the values and 1, is said to be developed, i 
when it is reduced to the form a x -f- b (1 — x), a and b being 
so determined as to make the result equivalent to the function 
whence it is derived. The following out of this development 
is purely algebraical, and occupies a good many pages of the 
work. To a student versed in ordinary Algebraical equations, 
the whole is sufficiently intelligible. We shall here indicate 
merely the results and applications. The following is given 
as an example. It is a definition with two defining marks. 
1 Clean beasts are such as both divide the hoof and chew the 
cud.' 

Let x = clean beasts, 

y = beasts dividing the hoof, 

z -= beasts chewing the cud. 
The definition will then be represented by the equation 

x = yz, 
which may be reduced to the form 

x — y z = 0, 
Here a function of x, y, and s, namely x — yz has to be 
developed according to the methods laid down. As a speci- 
men, we may transcribe the development ; 

JNow all those terms that are multiplied bv necessarily 
vanish and the remaining terms are 

^wi"f )= ° , ^ (1 ^ )=0 ' a7 ( 1 ^2/)( 1 -^=° J ( 1 --^^=0. 
Which equations all express the denial, or nothingness, of 
the combinations given in the left side of each.' Thus x y .' 
y~ 7 T means that there cannot be beasts that are clean 
O and that divide the hoof (y), and that do not chew the 

Tt ( Li ! ' S ° ^ l f St ° f the f0ar ' ( l - »)**** 0, indi- 
cates that there are no beasts unclean (1 _ x ) and yet divid- 
wg the hoof (y), and chewing the cud (z). 

These equivalent forms are somewhat obvious in themselves 
without the aid of analysis; but the author evolves more 
complicated equivalents, such as these :-< Unclean beasts are 



EQUIVALENT FORMS. 201 

all that divide the hoof without chewing the end, all that chew 
the cud without dividing the hoof, and all that neither divide 
the hoof nor chew the cud.' The reader may be curious to 
6ee the corresponding equation : — 

1 _ X = y (1 _ z) + Z (1 _ y) +( J _ y) (1 _ g y 

It is obvious, from this instance, that, out of a definition 
containing three or four defining marks (Senior's definition of 
wealth, for example), a great many equivalent forms are deriv- 
able. Whether there be any important form that the unassisted 
mind might not evolve, is not quite apparent. It is possible, 
however, that cases might arise where the symbolical method 
would yield equivalents too recondite for an intellect with 
only the ordinary logical training. 

The author extends his analysis so as to comprise a more 
difficult order of examples, typified thus. Suppose the analysis 
of a particular class of substances has conducted us to the 
following general conclusions, namely :— 

First. Wherever the properties A and B are combined, 
either the property C or the property D is present also ; but 
they are not present jointly. 

Secondly. Wherever B and C are combined, A and D are 
either both present or both absent. 

Thirdly. Wherever A and B are both absent, C and D are 
both absent also ; and vice versa, where C and D are both 
absent, A and D are both absent also. 

Let it then be required from these conditions to determine 
what may be concluded in any particular instance from the 
presence of the property A, with respect to the presence or 
absence of the properties B and C, paying no regard to the 
property D. The working of the corresponding equations 
leads to this answer : — Wherever A is present, there either C 
is present and B absent^ or C is absent. And, inversely, 
wherever C is present and A is absent, there A is present. 

Several other curious combinations might be quoted, still 
growing out of the equivalence of simple propositions. We 
are next led to the consideration of Secondary Propositions 
(hypotheticals, &c), which the author symbolizes by introduc- 
ing the idea of Time as their peculiarity. A simple, unqualified 
proposition (affirmative) holds through all time ; a negative, 
through no time ; a qualified proposition holds only through 
a certain limited time. The symbol 1 may represent an 
unqualified truth, as being true through the whole universe of 
time ; will stand for an unqualified negation, something true 
for no time. Let X represent a certain proposition, and let * 



202 BOOLE'S ADD1TONS TO THE SYLLOGISM. 

represent the time of its being true. So, if T represent 
another proposition, y may be taken for the time of its being 
true Taking both propositions together, x + y will denote the 
negate oAhe times when both X and Y are respectively 
true, those times being separated from each other. ^ Again, 

x ' y ma y denote a remainder of time left when the time y is 

taken from the time x, it being supposed that x includes?/. 
g Q x __ y w in indicate that X and Y are true for identical 
times. Further, x y indicates the portion of time when X and 
Y are both true. 

Now, as x denotes the time of X's being true, 1 — x will 
denote the time that X is false. So x (1 — y) will denote the 
time when X is true and Y is false : and so on. The same 
system is to be applied to any number of symbols. 

To express the proposition *X is true* (there being no limit 
or qualification), we have 

x = 1. 

To express the proposition ? X is false — .' 
x = 0. 

To express — * Either the proposition X is true or the propo- 
sition Y is true (not both).' First, ' When X is true Y is 
false,' is signified by # (1 — y) ; ' when Y is true X is false/ 
is signified by y (1 — - x) : the equation then is 

* (1-2/) +2/(1 -*) = !• 

Next to express the conditional Proposition, i If the proposi- 
tion Y is true, the proposition X is true/ This implies that 
whenever Y is true, X is true ; or that the time of the truth of 
X covers the whole time of the truth of Y, and possibly more. 
Hence X is at least equal to, if not larger than Y. Conse- 
quently some form must be given, implying that Y is contained 
in X : a form analogous to that required for a universal affir- 
mative proposition. Let v represent an indefinite portion of 
time, such as to express the unknown part of a whole, ' some, 
it may be — all/ and the equation required is 

y =z v x. 

It is unnecessary to exemplify the symbolism for the more 
complicated cases. The author is so far carried away by the 
success of his expedient for expressing compound or secondary 
propositions by a reference to time, that he speculates on an 
analogous mode of expressing the primary propositions by a 
reference to space ; and thinks that he thus lends some coun- 
tenance to the doctrine that Space and Time are 'forms of the 
human understanding.' 

A chapter is devoted to the treatment of the secondary pro- 






ENUMERATION OF PROPOSITIONS. 203 



positions, by way of exhausting their whole implication, in the 
maimer previously shewn for the primary propositions; the 
effect being, however, merely to deduce the usual consequences 
of disjunctive and of conditional assumptions. It is to bo 
remarked that the process is still one of immediate inference, 
confirming the view that in hypothetical syllogisms so-called, 
there is no real or mediate inference. 

In order to exhibit the value of the symbolical evolution of 
equivalent forms, Boole selects for analysis two specimens of 
metaphysical argumentation, sufficiently perplexing to test the 
powers of a logical method. They are (1) a portion of Samuel 
Clarke's ' Demonstration of the Being and Attributes of God,' 
and (2) Spinoza's argument to prove the identity of God and 
the Universe. He confessed that one main difficulty in dealing 
with those arguments is to extricate the real premises of the 
authors ; he might have added the farther difficulty of assign- 
ing definite and consistent meanings to the very abstract terras 
made use of by them — necessity, existence, eternity, cause, &c. 
But the premises once obtained, it is possible to embody them 
in symbols, and then to extract all their equivalents by solving 
the corresponding equations. The method may be commended 
as an interesting effort, varying and corroborating the method 
followed by a logical and acute mind working upon the ipsa 
corpora of the premises, without symbolism. 

We have now reviewed the larger half of Boole's work, and 
as yet have seen no mention of the svllogism. A short chapter 
is all that is bestowed upon mediate inference ; which, how- 
ever, is a mere carrying out of the algebraic method, with the 
modifications demanded by the nature of the case. 

He begins by accepting De Morgan's additions to the four 

types of propositions in the common Logic. He lays out the 

eight forms, with his equations for them : expressing the four 

new forms by supplying a contrary subject to each of the old 

forms. The parallelism is shown thus 

A — All Ys are Xs y = v x (1) 

(A) All not-Ys are Xs \ — y =z v x (2) 

E No Ys are Xs y = v (1 — x) (3) 

(E) No not-Ys are Xs 1 — y = v (1 — x) (4t) 

= < All Xs are Ys x = v y > 

I Some Ys are Xs v y = v x (5) 

(I) Some not-Ys are Xs v (1 — y) = v x (C) 

I 



204 BOOLE'S ADDITIONS TO THE SYLLOGISM. 

= -J Some Xs are not Ts v y = i> (1 — y) j 

O Some Ts are not Xs v y = v (I — x) (7) 

(O) Some not-Ys are not-Xs v (I — y) = « .(1 — ») (8) 

The second form of E coincides with A by mere transposition 
of letters. The second form of I is 0, in like manner. The 
second form of (0) is the only new form— Some not-Ys are 
not-Xs, some things are neither Ys nor Xs. This is one of 
Do Morgan's two disjunctives ; his other disjunctive — no 
not-X is not Y, every thing is either X or Y — does not appear 
in the above list. 

The laws of Conversion follow from the symbolical forms. 
The proposition ■ All Ys are Xs ' being represented by 
y — v cr, we have only to read v x — y, Some Xs are Ys. To 
convert the same proposition by negation (obversion and con- 
version), we deduce, by eliminating v t 
2/(1— a) = 
which gives by solution with reference to 1 — a?, 

i — * = o( 1 — y)> 

whose interpretation is ' All not-Xs are not-Ys. [This opera- 
tion contains methods and symbols not explained in the fore- 
going abstract]. 

So far as Conversion goes, the author merely continues his 
former methods of reducing and interpreting equations ; as we 
might expect from considering that conversion is merely one 
variety of Immediate or Equivalent Inference. The syllogism 
demands a step in advance. The two premises must be em- 
bodied in two equations, with a common middle term, and that 
term must be made to disappear in a third formed out of these 
two. • Thus, 

All Xs are Ys x = v y 

All Ys are Zs y = <o f z. 

Whence, by substituting for y, in the first equation, its 
value in the second, we have 

All Xs are Zs x = v v' z. 

The form v v'z shows that x is a part of a part of z. So with 
all other cases ; it is requisite merely to eliminate the middle 
term y. The method might be easily carried through the 
whole of the ordinary syllogisms ; as well as applied to the un- 
figured and fallacious forms. But the author proceeds to 
deduce the general rules of the syllogism by an equation com- 
prehending all the forms of valid reasoning. He gives as the 
results of the analysis these rules : ' when one middle term, at 



KULES OF THE SYLLOGISM. 205 

least is universal, equate the extremes/ * In case of unlike 
middle terms (one positive and the other negative), with one 
universal extreme, change the quantity and quality of that, 
extreme, and equate the result to the other extreme; ; and with 
two universal middle terms, change the quantity and the 
quality of either extreme, and equate the result to the other 
extreme unchanged/ 
Suppose the case — 

All Ys are Xs 
All Zs are Ys. 
This belongs to the first rule. * All Ys ' is the universal 
middle term ; the extremes being equated give as the conclu- 
sion, 

All Zs are Xs. 
Suppose next — 

All Xs are Ys 
No Zs are Ys. 
The proper expression of these premises is— 
All Xs are Ys 
All Zs are not-Ys. 
They belong to the case of unlike middle terms, and have 
one universal extreme. Whence, by application of the rule, 
we change the quality and the quantity of that extreme, and 
equate it with the other extreme — 

All Xs are not Zs, or No Xs are Zs. 
Commencing from the other universal extreme, we obtain 
the equivalent result — 

No Zs are Xs. 
A third case — 

All Ys are Xs 
All not-Ys are Zs. 
Here the terms are of unlike quality. There are two uni- 
versal middle terms, and, by the rule, we change the quantity 
and the quality of either extreme (Some Xs into All not-Xs), 
and equate with the other extreme (Some Zs). 
All not-Xs are Zs. 
The two last examples are selected by the author as present- 
ing syllogisms that would not be regarded as valid in the 
Scholastic Logic, which virtually requires that the subject of a 
proposition should be positive. [As often remarked already, 
the want of a thorough-going recognition of contraries is the 
defect of the Aristotelian scheme]. The cases are, however, 
perfectly legitimate in themselves, and the rules for determin- 
ing them are undoubtedly the most general canons of syllogisO* 



206 BOOLE'S ADDITIONS TO THE SYLLOGISM. 

inference. The analysis employed, the author contends, is not 
properly of the syllogism, but of a much more general mode 
of combining propositions to yield results; and he gives an 
imaginary case to illustrate this wider import. 

Without pursuing the syllogism farther, Boole now dis- 
cusses the vexed question as to the fundamental t} r pe of de- 
ductive reasoning, and takes issue with Whately and with 
Mill, who agree in this that all valid ratiocination is ultimately 
the inferring of propositions from others of a more general 
kind ; the syllogism being a full and adequate formal repre- 
sentation of the process. Now, as the Syllogism is a species 
of elimination, the question resolves itself into these two deter- 
minations, namely, first, whether all elimination is reducible 
to Syllogism ; and, secondly, whether deductive reasoning 
consists only of elimination. 

To the first question, he replies, that it is always theoreti- 
cally possible so to resolve and to combine propositions that 
elimination may subsequently be effected by the syllogistic 
canons, but that the process of reduction would, in many cases, 
be constrained and unnatural, and would involve operations 
that are not syllogistic. 

To the second question, he replies that reasoning cannot, ex- , 
cept by arbitrary restriction, be confined to elimination. It 
cannot be less than the aggregate of the methods founded on 
the Laws of Thought, and the process of elimination, import- 
ant as it is, is only one process among others. 

He farther remarks that, of all the Laws of Thought, the 
one of fundamental importance in Logic, is the Law of Con- 
tradiction, to which Leibnitz also assigned the same position. 

All persons that have attained a just notion of the Rela- 
tivity of Knowledge, would agree with Boole in the prime im- 
portance thus given to Contrariety or Contradiction; but this 
merely goes the length of Equivalence or Immediate Inference. 
It prepares the way for Syllogism, and is the main key to the 
useful enlargements of the syllogism ; but it does not touch 
what is essential to deduction. The axiom, or ' law of thought/ 
at the foundation of mediate inference must be something else, 
and if it is not the axiom assigned in the previous chapter of 
this work, it is an axiom yet to be sought. Passing from Boole's 
somewhat vague generalities to his actual method, which con- 
sists in combining two equations standing for the premises of 
the syllogism, into a third standing for the conclusion ; and 
adverting to the maxim that justifies the process of reduction, 



AXIOM OF THE SYLLOGISM. 207 

we 6eem to see that it is the same maxim as enters into a pro- 
blem of equations with two or more unknown quantities ; as 
for example, given x + y = a, x — y =. b, to find x and y. 
Grant that the conditions of a logical syllogism are fairly ex- 
pressed by Boole's symbols, and that the algebraic reduction is 
suitable and relevant to the case, then the logical axiom is the 
algebraic axiom that permits the substituting for y in one 
equation, of its equivalent in the other ; as when we obtain from 
x — y — b, y = x — &, and insert this value of y in the equa- 
tion x -{- y = a* The axiom of direct application to the 
case would be that, for any quantity, its equivalent may be 
substituted in an equation ; in other words, the substitution, 
for any quantity, of its equivalent, does not change the value 
of the equation. This is a various reading of the axiom of 
mediate equality — things equal to the same thing are equal to 
one another ; an axiom to which Mr. Mill compares, in point 
of form, the axiom of the syllogism. If one thing is equal to 
a second, and the second equal to a third, the first is also equal 
to the third. In a combination containing A and B, we may 
introduce in room of B its equivalent C. 

A large portion of the work is devoted to Probabilities, in 
handling which, the author continues the symbolism employed 
in the previous portion of the work. It is generally admitted 
that he has made important additions to the theory of thia 
subject, the common ground of Mathematics and of Logic. 



CHAPTER IIL 
FUNCTIONS AND VALUE OF THE SYLLOGISM. 

1. It is the peculiarity of the Syllogism, that the conclu- 
sion does not advance beyond the premises. This circum- 
stance has been viewed in two lights. 

On the one hand, it is regarded as the characteristic 
excellence of the Syllogism. 

On the other hand, it is represented as constituting a 
petitio principii. 

In the syllogism 'men are mortal, kings are men, kings are 
mortal.' the conclusion seems already affirmed in the premises. 

i 



208 FUNCTIONS AND VALUE OF THE SYLLOGISM. 

By virtue of the universal major, coupled with the interpreting 
minor, there is distinctly involved in the premises the fact that 
4 kings are mortal.' 

(1) To this circumstance Las been attributed the peculiar 
excellence, dignity, and certainty of syllogistic inference. 
When the two premises are supplied, the conclusion cannot be 
refused without self-contradiction. There is nothing precarious 
in the leap from the premises to the conclusion. 

The same circumstance has been represented in a more dis- 
advantageous light. The allegation is made that mere repeti- 
tion is not inference : that to reproduce in a new form what is 
already given may be highly convenient (as in the various 
kinds of Immediate Inference), but is no march, no progress 
from the known to the unknown. 

(2) There remains a far more serious charge, and one that 
takes us direct to the root of Formal Reasoning. Supposing 
there were any doubt as to the conclusion that kings are mortal, 
by what. right do we proclaim, in the major, that all men are 
mortal, kings included ? 

It would be requisite, seemingly, to establish the conclusion 
before we can establish the major. In order to say, ' All men 
are mortal/ we must have found, in some other way, that all 
kings, and all peoples are mortal. So that the conclusion first 
contributes its quota to the major premise, and then takes it 
back again. 

This is the deadlock of the syllogism, the circumstance that 
has brought down upon it the charge of * reasoning in a circle * 
{petitio principii). In point of fact, we can hardly produce a 
more glaring case of that fallacy. 

The extrication from the puzzle is due to Mr. John Stuart 
Mill, and the consequence has been a total revolution in Logic. 

2. The major premise of a syllogism (in the regular 
figure) may, so far as the evidence is concerned, be divided 
into two parts ; the one part containing the instances 
observed, and the other part containing the instances not 
observed, but inferred. 

The major premise, 'All men are mortal,' consists of two 
very different statements. The first is, that a certain number 
of men have actually died. The evidence for these is actual 
observation, the highest of all evidence. The second statement 
is, that the men now living, and the men yet to be born, will 
die ; for which there is not the evidence of observation. 

In the same manner may we analyze any other general 



REASONING IS FROM PARTICULARS TO PARTICULARS. 209 

affirmation or negation. The proposition * transparent bodies 
bend light ' is made up of the bodies that have been act 
experimented on, and of bodies that have not been ex pen- 
mented on; in the one case, the predicate is affirmed on tho 
evidence of fact; in the other case, the predicate is affirmed by 
virtue of the inductive leap from the known to the unknown. 

Thus, the ordinary form of the general proposition confounds 
together the observed with the unobserved ; the indiscriminate 
fusion of the two is what has perplexed the theory of tho 
syllogism. 

3. In affirming a general proposition, real Inference is 
exhausted. 

When we have said 'AH men are mortal/ we have made 
the greatest possible stretch of inference. We have affirmed 
mortality of all men, of every class, in every age, past and 
future. We have incurred the utmost peril of the inductive 
hazard. Whatever justification needs to be offered for the 
inference in hand, must be advanced as a security for the 
major premise. 

4. The type of reasoning that best discloses the real 
process is reasoning from Particulars to Particulars. 

The basis of fact in every argument may be stated to be 
the particulars actually known from experience ; as the mor- 
tality of the men that have died. The inference is usually to 
some other particulars unobserved, as 'the present inhabitants 
of London will die.' The real evidence for the mortality of 
the men now living is the death of their predecessors. A, B, 
and C, have died ; D, now living, will die. 

The practice of reasoning at once from certain particulars 
experienced, to some other particular as yet unexperienced, 
(there being a similarity in the cases) is not only the usual, 
but the most obvious and ready method. We feel that the 
real force of every reasoning lies not in the general statement, 
but in the actual facts ; and we are as much moved by the 
facts in their particularity, as when they are given in a gene- 
rality. That boiling water will scald the hand, is sufficiently 
proved by its having done so in innumerable past instances ; 
the deterring force lies in these actual instances. We are in- 
fluenced by individual precedents, as strongly as by rules. 

This is seen extensively in all professions. The experience 
of a professional man consists of the cases he has actually ob- 



210 FUNCTIONS AND VALUE OF THE SYLLOGISM. 

served ; these he remembers as particulars, and when a new 
example is presented, he at once assimilates that with the pre- 
vious particulars, and infers accordingly. When Dr. Mead 
was called in to the last illness of Queen Mary, he pronounced 
the disease to be small pox ; his knowledge of that ailment 
was the remembrance of a series of patients previously wit- 
nessed by him ; the queen's symptoms resembled those, and he 
drew the inference. 

5. Wherever we may infer from a certain number of 
particulars given, to one other particular, we may infer to 
a whole class, or make the inference general. 

If we can infer, from the men that have died, that the pre- 
sent Pope will die, it is by virtue of a sufficient amount of re- 
semblance between them and him ; and we must be prepared 
to make ihe same inference in all other cases where the re- 
semblance holds. We may, therefore, say once for all, whoever 
resembles past generations of human beings, in the points 
wherein the pope resembles them, will die. The justification 
of one is the justification of the whole. The inference to an 
individual case must not be arbitrary ; it must be grounded on 
a resemblance, and be applicable wherever the resemblance is 
found. 

In a general proposition, therefore, we state the points of 
resemblance that entitle us to infer from past particulars to a 
new particular ; and in stating these points we render the in- 
ference at once general, and formally exhaustive. We mingle 
up in one statement the observed known, and the inferred 
unknown, the evidence and the conclusions. The use of 
general language enables us thus to rise beyond particular 
inferences. 

6. Deductive Inference may be described as a process of 
Interpretation. 

Although the major premise covers the conclusion, it does 
not point to it by name, but only by character. The premise 
* men are mortal ' does not specify kings, nor the living pope ; 
it indicates certain marks by which we are to judge whether 
kiugs and popes are to be pronounced mortal, namely, the 
marks of 'men or humanity.' Something, therefore, is want- 
ing, in addition to the major premise, in order to the conclu- 
sion, the pope is mortal ; we have to be assured that he is a 
man, that he conforms to the defining marks of human beings. 
To supply this requisite is the purpose of the minor premise, 



DEDUCTIVE INFERENCE IS INTERPRETATION 211 

which declares that the pope possesses the attributes of mm 
or identifies him with the subject of the major premise. The 
necessity for such an affirmation rescues the syllogism from 
Immediate Inference or tautology. 4 All men are mortal ' in- 
cludes 'the pope is mortal/ on the supposition that the pope [g 
a man ; and if this supposition is explicitly given in a distinct 
proposition, the pope is then brought within the sweep of the 
major premise : and the conclusion is established. 

After affirming a general proposition (or making a general 
denial) connecting or disconnecting a certain subject with a 
certain predicate — men and mortality— we have still to hunt 
out the particular cases of the subject, the things that possess 
its attributes. This is the real deduction, and it is a material 
and not a formal process. It is an operation of comparing the 
actual individuals already pointed out by the generalized subject 
— actual and known men — with all future individuals as they 
occur, and of pronouncing agreement of the new with the old. 
The deductive inference that ' the pope is mortal/ presupposes 
an examination (direct or indirect) of the pope's personality. 
If this resembles the usual type of humanity, judged from the 
instances actually known to us, we identify him with the 
subject, 'men/ in our general proposition. The identity being 
considered satisfactory, we complete the syllogistic formula, 
and declare him to be mortal. 

The proposition 'men are mortal,' by its form of universality, 
imposes upon us, and leads us to suppose that we have in our 
grasp the whole human race. The correcter view is to regard 
it as an allegation respecting a certain number, with a power 
of including others as they come on the stage. The proposition 
assigns marks for the future identification of the beings that 
are to be declared mortal ; and, as the identification proceeds, 
the minor premise is replenished with appropriate cases, and 
so brings forth the conclusion. 

The interpretation of a law or a command illustrates the 
purely deductive part of the operation of reasoning — the sup- 
plying of the minor. The law is given in general terms ; cer- 
tain characters are assigned as belonging to the subject of the 
proposition. The administrator or judge ascertains whether 
any particular case has or has not the characters specified. If 
it has, a minor proposition is afforded, and a conclusion is 
drawn. 

This case also shows that the syllogism is the mere formal 
completing of an operation, not at all formal, but in the strict 
sense material. The operation consists in comparing one par- 



212 FUNCTIONS AND VALUE OF THE SYLLOGISM. 

ticular fact with other particular facts, through the medium of 
a general description. The wording of a law, however gene- 
ral be the terms, must be such as to suggest definite individual 
cases. When the law mentions heritable property, or person- 
alty, it must either state or suggest the -particular 'things in- 
tended ; and the question of the application to a given case 
turns upon the comparison of the case with the cases cited 
or snggested by the general term or definition. Hence, the 
business of the reasoner, in actual practice, is concrete com- 
parisov, from which, in the last resort, he can never be ex- 
empted. This is material deduction, which, in its essence, is the 
same as material induction, being the carrying out of the in- 
ductive operation, or the in-gathering of the details shadowed 
forth, but not actually seen, in the general proposition. 

Legal decisions are founded sometimes on statutes, some- 
times on precedents or previous decisions. There is no generic 
distinction between the two modes. A statute has no meaning 
except the particular cases specified or suggested; and a pre- 
cedent must involve a principle or rule. In both, the judge 
refers back to concrete particulars, which are viewed under a 
certain point of likeness or community. 

Another case is the application of general theorems furnished 
by the observations of others, such as the principles of science 
established by foregone researches. We may have had no 
share in arriving at the induction known as the atomic theory ; 
we have not even seen the facts, we receive them embodied 
and registered in the general statement of the law. We must 
understand the meaning of that statement; we must realize 
the kind of facts intended by it. When a case is started, a 
given compound of two substances, we must say, by concrete 
comparison, whether this compound has the characters of the 
compounds expressed as chemical compounds. For example, 
is the atmosphere a chemical compound ? Does it agree with 
the general characters of chemical compounds, or with those 
typical instances that the general characters can do nothing 
but refer us to. This is a truly material deduction ; it is that 
process of comparing instances that is the essence of the 
generalizing operation, as seen' in induction. It exactly 
resembles generalization with a view to definition. 

7. Although the deductive stage of induction is still an 
inference from particulars to particulars, which nothing 
can supersede, there are certain advantages in embodying 
the possible inferences in a formal generality. 



UTILITY OF THE SYLLOGISM. 213 

Mr. Mill remarks that the syllogistic form of inference, from 
generals to particulars, which supposes that each induction 
is made general, is ' a collateral security for the correct] u 
the generalization itself.' It is so in two ways. 

First. It increases the sense of responsibility on the part of 
the reasoner, by letting him know that his inference to one 
individual must equally apply to a large host of individuals. 
A common device for checking a rash inference is to point out 
the extent of the consequences involved. The legal decision 
against John Hampden, in the matter of thirty shillings of 
ship money, was portentous as affirming the king's power to 
tax the nation without a parliament 

Secondly. If an induction is unsound, the making it 
general is likely to suggest contradictory instances. This is 
merely a modification of the same consequence. Any person 
attempting to justify a particular despotism must be prepared 
to say that, in all similar circumstances, despotism would be 
desirable. The remark is sometimes made, in the controversy 
as to the inspiration of the Bible, that even Milton was 
inspired ; but, if so, then all great poets— Homer, Virgil, 
Dante, Chaucer, Shakespeare, Dry den, Byron, Shelley — must 
also own the gift of inspiration. 

Mr. Grote,. in defending the received canon of the Platonic 
writings from the critics that would reject many of the Dia- 
logues, on the ground of their style being unworthy of Plato, 
points out the numerous Dialogues that would have to be 
sacrificed to this criterion, if each critic were allowed to reject 
for himself, and all rejections were admitted. 

8. One great use of the syllogistic form is to analyze, 
bring to light, and present for separate consideration, the 
parts of a step or a chain of reasoning. 

This has been already exemplified in the applications of the 
syllogism to confused reasonings. It is advantageous to know 
that the truth of a conclusion by inference supposes the truth 
of two separate allegations, both alike necessary to the conclu- 
sion. To prove that A is C, by a mediate inference (B is C, 
A is B), two propositions have to be verified ; and the mind is 
aided in disentangling a perplexed argumentation, by knowing 
what to look out for. 

In stating the distinction between the two modes of reasoning, 
used both in Law and in Politics — reasoning from Precedents or 
Examples, and reasoning from Eules or Principles — Sir G. C. 
Lewis adverts to the great superiority of the last, the reasoning 



214 TRAINS OF REASONING AND DEDUCTIVE SCIENCES. 

from Rules. The reason of the comparative obscurity of the 
argument from example or precedent, is that the principle involved 
is usually suppressed. 4 The reasoning is much more perspicuous 
when the general principle is stated first, the particular case is 
placed under it, and the conclusion is then drawn. In order to 
argue from one case to another, it is necessary to reject from each 
the circumstances immaterial to the matter in hand, and to 
compare those in which they agree. In complex cases, this process 
is often extremely difficult. Much sagacity and knowledge of the 
subject are required, in order to discriminate between material 
and immaterial facts — to reject enough, but not more than 
enough. For if immaterial facts are retained, the comparison 
becomes obscure and uncertain ; if material facts are rejected, it 
becomes fallacious. Thi3 process, which, in the argument from 
precedent, must often be performed mentally, though it may be 
easy and sure to the experienced practician, perplexes the tiro. 
Hence, students of the law have great difficulty in collecting legal 
rules from cases, though they are soon able to apply a rule of law, 
laid down in general terms, to a particular case of practice.' 



CHAPTER IV. 
TKAINS OF SEASONING AND DEDUCTIVE SCIENCES. 

1. A series of syllogisms may be connected in a chain. 

Logicians have always recognized compound reasonings. 
The Sorites is a connected chain of syllogisms. The conclusion 
of one syllogism may be the major premise to a second, and so on. 
The Sorites is usually stated in this form : — 

A is B, B is C, C is D, &c, therefore A is D. 
_ The regular form of proof (by the First Figure of the Syllo- 
gism*) is — 

B is C, A is B, therefore A is C. 

C is D, A is C, therefore A is D, &c. 
It can scarcely ever happen that a proper deduction in this 
simple form can be protracted over two or three syllogisms. 
The application of a universal proposition to a particular case 
seldom needs to descend by three or more distinct steps: 
indeed, in by far the greater number of instances, the descent 
is made at once. 

No new logical principle, or modification of principle, is 
involved in these consecutive reasonings. Their lucid state- 

I 



EXAMPLE OF A CHAIN. 214 

ment is a matter of consideration for the expositor, but thoy 
present no speciality to the logician. Still, they are usually 
discussed in treatises on logic ; and we may, following the 
example of Mr. Mill, take occasion from them to discuss two 
themes — the compatibility of the foregoing theory of the syllo- 
gism with such trains, and the nature of the Deductive 
Sciences. 

' 2. A chain of Reasoning is reducible to a series of syllo- 
gisms, the major in each being an induction from par- 
ticulars, or a truth ultimately based in particulars. 

Thus, if we were to prove that intelligent beings, although 
they may be interrogated, are not to be experimented on like 
brute matter, we should have the following chain : — wherever 
there is intelligence, there is sensibility, in other words, suscepti- 
bility to pleasure and pain ; we are not at liberty to intLct pain ; 
now, most experiments that could be tried upon sentient crea- 
tures would be painful ; hence, intelligent beings are not lit 
6ubjects for experimental enquiry. Three syllogisms are con- 
cerned in this chain of reasoning. The majors are — 

( 1 ) Society prohibits the infliction of pain. 

(2) All intelligent beings have sensibility to pain. 

(3) Experiments for ascertaining function in sentient beings 
lead to pain. 

Each of these majors may be resolved, according to the 
method of the previous chapter, into particulars observed and 
particulars inferred, or left to be inferred, by virtue of identity. 
The first major (Society prohibits) is in the form of a command, 
the case where we may be supposed to be least concerned with 
the particulars, and most concerned with the general descrip- 
tion serving to identify the particulars. Still it must not be 
forgotten that the real force even of a command is embodied 
in the instances where it is enforced ; the general state- 
ment means nothing, is nothing, except as referring us to 
these; the application of the rule is an inductive extension 
of these instances. The second major (intelligent beings have 
Kensibility) takes in the observed coincidences of intelligence 
and sensibility, together with the future extensions of these by 
identification with the presence of intelligence — the first term 
of the couple. The third major is likewise an inductive gene- 
ralization, containing the observed particulars where experi- 
menting has ended in pain, together with the resembling 
inferred particulars. 

We may arrange the train of reasoning in syllogisms. Thus, 
— taking a different order — 



216 TKAINS OF REASONING AND DEDUCTIVE SCIENCES. 

First Syllogism. 
Experiments for ascertaining function in sentient creatures 

lead to pain. . ' 

Tbo present proposal is an experiment for ascertaining 

function. 
The present proposal will lead to pain (Barbara). 

Second Syllogism. 

Society prohibits the infliction of pain. 
The present proposal will lead to pain. 
Society prohibits the proposal to experiment on sentient 
beings (Cesar e). 

Third Syllogism. 

Society prohibits experiments on sentient beings. 

All intelligent beings are sentient beings. 

Society prohibits experiments on intelligent beings. (Cesare). 
The form (Society prohibits, &c), has the force of a nega- 
tive ; were it not so, the last syllogism would not be valid. 

The language of inference from particulars to particulars 
might be used in each of these syllogisms. Thus in the first : 
Experiments for ascertaining function in sensitive beings have 
been observed to lead to pain ; the present case is an experi- 
ment for ascertaining function : the present case will lead to 
pain (as the observed cases have done). Similarly for the 
others. 

The Deductive Sciences. 

3. The Deductive Sciences are those where the labour 
mainly lies in applying or carrying out ascertained induc- 
tions, that is, in the discovery of minors to given majors. 

From the foregoing theory of the syllogism, it is apparent 
that every deduction supposes a previous induction. The 
Deductive Sciences, therefore, do not dispense with induction. 
Whereas, in the Inductive Sciences, such as Chemistry and 
Physiology, the chief labour consists in arriving at inductions ; 
in the Deductive Sciences, as Mathematics, the inductions are 
few and easily gained (being in fact sometimes called intui- 
tions) and the labour consists in carrying them out into their 
various applications, by bringing cases nnder them. We soon 
arriveat the inductions 'things equal to the same thing are 
equal,' or 'the sums of equals are equal ; ' 'the differences of 






GEOMETRICAL DEDUCTION. 217 

equals are equal : ' but it was not easy to bring under the B 
of these inductions the proposition 4 a sphere is equal to two- 
thirds of the circumscribed cylinder.' This is arrived at only 
after a long and circuitous process of successive deductions, 
based upon the invention of numerous diagrams. 

If we take a comparatively simple case of geometric deduc- 
tion, the 47th of the First Book of Euclid, ' the square des- 
cribed on the hypo then use of a right-angled triangle is equal to 
the sum of the squares described on the two sides,' we shall find 
that the proof can be accomplished by two main leaps — two 
syllogisms having axiomatic* majors, and a preparatory syllo- 
gism having as its major a previously established deiivativo 
proposition. The rest of the process is not syllogistic. We 
first, by an ingeniously devised construction, establish two 
minors under the proposition — f A parallelogram and a triangle 
being on the same base and between the same parallels, the 
parallelogram is double of the triangle ; ! and then proceed to 
the main steps, the application of the axioms. We first apply 
the axiom — ' The doubles of equals are equal,' (a derivative 
from the axiom — 'The sums of equals are equal,') to prove 
that the square described on one of the sides is equal to a part 
of the hypothenuse square, and that the square described on 
the other side is equal to the remaining part of the hypothen- 
use square. This being done, it needs but an easy application 
of the axiom — ' The sums of equals are equal/ to complete the 
proof. 

The deductive sciences circumvent their problems ; they 
accomplish indirectly what there is no means of accomplishing 
directly. The science of mathematics instead of resting satis- 
fied with announcing its axioms and definitions, and leaving 
people to apply them at once, evolves a vast scheme of deductive 
properties, to any one of which we may repair in an emergency, 
instead of making a connexion at once with the fountain head. 
We measure a height by bringing the case under some theorem 
of Plane Trigonometry that chances to be adapted to the 
means at our command. 

The length and the complicacy of mathematical or other 
reasonings may be ascribed to these two circumstances. 

(1) There are many steps of mere Immediate Inference, as 
in applying Definitions. Thus, when Euclid shows that two 
figures coincide, he makes a formal appeal to the Definition of 
Equality (namely, Coincidence), and, by virtue of that declares 
them to be equal. This is seemingly a step in the reasoning ; 
it involves a distinct act of attention on the part of the stu- 



218 TRAINS OF MASONING AND DEDUCTIVE SCIENCES. 

dent, but it is not a deduction or syllogism. So, there may be 
Ftcps involving other transitions to Equivalent Forms, as Ob* 
version, Conversion, &c. 

(2) Not only is a great deal of preparatory construction or 
scaffolding often required in order to bring the case under tho 
sweep of a previous generality, but, when the construction is 
made, there jut out from every part of it separate inferences, 
and all these have to be made convergent to the purpose in 
hand. Moreover, many propositions start at once with a com- 
plicated hypothesis — ' If a point be taken without a circle (1), 
and straight lines be drawn from it to the circumference (2), 
whereof one passes through the centre (3)/ &c. ; the proof in 
these cases is a convergent series of steps, each starting from 
a distinct member of the hypothesis. 

The process of Identification to supply a minor is difficult 
according to the complicacy of the subject of the major ; as in 
Diseases, in Law, in Politics, &c. A disease being character- 
ized by three, four, or five distinctive symptoms, must be 
identified on all these symptoms ; a failure in any one leaves 
the disease unidentified. Hence, deduction may be a work of 
labour even in the sciences of Induction, as Medicine must be 
pronounced to be. 

So, in Politics, Sir G. C. Lewis remarks that the difficulty 
may lie in bringing the Premises of the syllogism together, 
that is, in finding the major to a given minor, or the minor to 
a given major. * It is the subsumption of the minor under the 
major premise that really constitutes the originality, or inven- 
tion, of the argument.' The following is an example : — 

General Maxim, or Major — When a customs duty is so high 
as to produce extensive smuggling, it ought to be reduced. 

Particular case, or Minor — The existing customs duty, in 
country A, upon tobacco, or brandy, or hardware, &c, leads 
to extensive smuggling. 

Now, the minor is obviously a matter of fact (determined 
partly by reasonings from facts), and may take much trouble 
to establish. 

4 The special aim of Deduction is to ascertain every 
fact implied in facts already known. A Deductive deter- 
mination is opposed to an Experimental determination. 

When, by the application of ascertained inductions, we can 
discover new truths, we save the appeal to direct experiment. 
13y the parallelogram of forces, we can find the exact course 
ot any moving body urged in different directions by given 

\ 



PUSHING OF DEDUCTIONS. 219 

forces. A process of computation is substituted for a process 
of observation ; the consequence is, in most instances, a irrttt 
economy. ° 

The pushing of truths of induction to all their deductive 
applications is one great department of scientific research. 
The aptitude for the operation is almost purely intellectual. 
When a great law, such as Gravitation, has been established, 
the following out of all its deductive consequences supplies 
work to several generations of men. The generalization of 
the present day, called the Persistence of Force, will give pro- 
bably an equal amount of occupation to the more purely de- 
ductive or speculative aptitudes of the scientific mind. The 
inductive laws that connect Mind with Body, when ascertained 
with precision, will admit of being deductively pushed in 
numerous ways, and will yield many facts at present discover- 
able only by separate observations. The doctrine of the 
Relativity of all Feeling and Thought has not as yet been 
completely followed out to its consequences. 



CHAPTER V. 

DEMONSTRATION.— AXIOMS.— NECESSARY TRUTH. 

1. The kind of evidence named ' Demonstration ' has its 
sources in Induction. . 

Demonstrative proof is only another name for Deductive 
proof, which, in the last resort, is Induction. The propositions 
of Euclid are said to be demonstrated ; and, as above seen, this 
means that the conclusions are proved by bringing each case 
under the sweep of the fundamental principles of the science. 

To make out Mathematical Demonstration inductive, it is 
requisite to show — (1) that the foundations of the Science 
(the axioms) are inductive ; and (2) that the axiom of the 
Syllogism is inductive. The axioms of mathematics supply 
the principles, and the axiom of the syllogism justifies their 
application. 

In the question respecting the ultimate foundations of the 
so-called axioms, these are the chief examples in dispute. It 
is maintained, on one side, that the axioms of Mathematics, 



220 DEMONSTRATION.— AXIOMS.— NECESSARY TRUTH. 

the axiom of the Syllogism, together with the axiom of Causa- 
tion, -are inductions from particular facts of experience; and 
on the other side, that they are of intuitive origin, and, in this 
origin, possess a higher certainty than can be given by experi- 
ence. * 

2. The chief argument against the Inductive origin of 
these principles is that they are necessary, and no experi- 
ence can give the character of necessity. 

The idea of ' necessity/ as attaching to such truths as the 
mathematical axioms, dates from Leibnitz ; it was re-stated, 
in a qualified form, by Kant, and persists in the minds of many 
to the present day. The term, however, is ambiguous. 

Meanings of Necessity. 

3. T. In common speech, 'necessity' is a synonym of 
certainty ; and would apply to inductive truths. 

When speaking of anything that is certain to happen, we use 
among other words, the term * necessary/ We should call the 
freezing of water, at 32°, a necessity, meaning that we are 
perfectly sure of its happening. We even say that vice is a 
necessary consequence of bad training. 

The necessity in such cases has admittedly nothing to do 
with intuitive perception. Experience is competent, in every 
instance, to give the strong assurance that the word signifies. 
So, we have only experience to rely upon in believing that the 
sun must rise to-morrow. 

There could be nothing incompatible with this usage in 
terming all the inductive laws of nature i necessary .' — the law 
of gravity, the laws of motion, the fundamental laws of organi- 
sation, and so on. But metaphysicians are accustomed to call 
these principles * contingent/ as opposed to necessary ; for al- 
though they are true, as the universe is now constituted, they 
might have been otherwise. The law of gravity might have 
been wanting ; the laws of organized beings might have been 
different. But, in no circumstance (it is said) could ' two 
straight lines enclose a space ; ! this, therefore, is necessary in 
a more peculiar sense of the word, as will be next stated. 

* On the subject of Mathematical Evidence, other questions have been 
raised -namely, the place of the Definitions in the Science, and the sup- 
posed hypothetical character of definitions. These questions will be ad- 
verted to afterwards (Logic op the Scie>ces, Mathematics). 

I 






NECESSITY AS IMPLICATION. 221 



4. II. 'Necessity* more properly means implication; 
1 necessary truths ' in this seuse are the truths demanded 
by Consistency. Their denial is a contradiction in trims. 

These truths have already beeu fully exemplified. (See 
Introduction, and also Equivalent Pkopositional Foums). That 
tbe less cannot contain the greater, is necessary ; it follows 
from the very meaning of less and greater ; it could not be 
contradicted without declaring the greater not to be the 
greater. l The same thing cannot be in two places at once ' 
is necessary ; the meaning of a * place ' is some definite spot 
the negative of all other places ; to say that a thing is in a 
particular place is to deny that it is in a second, or a third, 
or any other place. * Time is an eternal now /' must be set 
down as self-contradictory. 

Some of the axioms of Euclid are necessary in this sense. 
4 A whole is greater than its part * is implicated in the defini- 
tion of whole and part ; it could not be contradicted without 
contradicting the definition. A whole is summed up by its 
parts ; omit any of these, and the whole is not made up ; the 
result is something less than the whole, 

* Things that coincide are equal ' is not an axiom but a de- 
finition ; it is the mark or test of equality, the only mark that 
can be propounded in the last resort. 

Of all the alleged necessary truths, the one most frequently 
cited in the present controversy is — 4 Two straight lines can- 
not enclose a space.' This was held by Kant to be a real pro- 
position, a synthetic judgment; in other words, the subject is 
not implied in the predicate ; to it the criterion of ' implica- 
tion' wonld, therefore, not apply. 

On the other hand, mathematicians are now probably unani- 
mous in regarding this as a corollary from the definition of 
the straight line, or as implicated in the very essence of 
straightness ; so that to deny it would be a contradiction in 
terms. They would characterize it, in Kant's own language, 
as an 4 analytic ' judgment. A very little reflection on the 
case proves that the mathematicians are right. Starting from 
the definition of the straight line — ' when two lines are such 
that they cannot coincide in two points without coinciding alto- 
gether, they are called straight lines/ we see that the very 
terms forbid the enclosing of a space ; what meaning can we 
attach to * coinciding altogether,' but the exclusion of non- 
coincidence, or of an intermediate space ? Total coincidence, 
and an intervening space, are wholly incompatible ; if the one 



222 DEMONSTRATION.— AXIOMS.— NECESSARY TRUTH. 

is true the other is false. The proposition is therefore neces- 
nry io the sense of implication, as much so as a ' straight 
line is not a bent line/ 'a whole is greater than its part/ 

The axiom * Things equal to the same thing are equal to 
one another ' is not a truth of implication, and therefore is not 
a necessary truth in the present sense. The subject and the 
predicate express distinct properties, and the one does not in- 
volve the other. The axiom declares that mediate coincidence 
is to be held as carrying with it, or as making, immediate 
coincidence ; but the two modes of coincidence are not iden- 
tical. It is immediate coincidence that makes equality, accord- 
ing to the definition of equality; the axiom extends this very 
narrow, and often inapplicable test, and declares that coin- 
cidence through some third thing, a go-between, will be found 
in the end to be the same as actual coincidence, and is conse- 
quently to be accepted in all cases as a test of equality. If, 
therefore, this axiom is to be held as a necessary truth, some 
other meaning than the present must be assigned to necessity. 

5. Necessary truths, in the foregoing signification, are so 
far independent of experience, that they are perceived to be 
true when the language is understood. They do not, how- 
ever, require any powers of intuitive perception. 

As soon as we fully comprehend the notion of whole and 
part, we perceive that the whole is greater than the part ; 
avo do not need to make observations and experiments to prove 
it. We required concrete experience, in the first instance, to 
attain to the notion of whole and part; but the notion once 
arrived at implies that the whole is greater. In fact, we could 
not have the notion without an experience tantamount to this 
conclusion. When we know a fact, we know it, even when 
called by another name, which is all that is meant, at present, 
by necessary truth. When we have mastered the notion of 
straightness, we have also mastered that aspect of it expressed 
by the affirmation, 'two straight lines cannot enclose a 
space.' 

No intuitive or innate powers or perceptions are needed for 
such cases. Our ordinary intellectual powers enable us to 
pronounce, in more than one form, that an object is everything 
or anything that we have found it to be. We cannot have the 
full meaning of ' straightness ' without going through a com- 
parison of straight objects among themselves, and with their 
opposites, bent or crooked objects. The result of this com- 
parison is, inter alia, that straightness in two lines is seen to 

I 



INCONCEIVABILITY OF TIIE OPPOSITE. 223 

be incompatible with enclosing a space ; the enclosure of space 
involves crookedness in at least one of the lines. 

6. III. A third meaning aud criterion of Necessity, is 
inconceivability of the opposite. 

It is maintained that • things equal to the same thing are 
equal to one another/ because the mind is unable to conceive 
things agreeing with a common standard, and yet not agree- 
ing when directly compared. It is also maintained that we 
are unable to conceive * effects arising without a cause ;' whence 
such propositions are declared to be true necessarily. The 
test of inconceivability of the opposite (strongly urged by 
Whewell, and held with modifications by Spencer), is liable to 
serious objections. What we can, or cannot conceive, is mani- 
festly dependent, in a very large measure, on our education : 
the proof of which is that many truths inconceivable in one 
age and country are not only conceivable under a different 
state of education, but are so thoroughly engrained that their 
opposites are inconceivable. The Greeks held matter to be 
eternal and self-existent ; many moderns hold that the self- 
existence of matter is inconceivable. Some maintain that 
mind is the only conceivable source of moving power or force ; 
others, regarding the action of mind upon matter as incon- 
ceivable, have contrived special hypotheses to get over the 
difficulty, — we may instance Malebranche's doctrine of Divioe 
Interference, and Leibnitz's Pre-established Harmony. New- 
ton could not conceive gravity without a medium. 

With regard to truths of Implication, the difficulty of con- 
ceiving the opposite must be at its maximum. Yet self-con- 
tradiction is not an impossible operation, for it is often done. 
In Theology, people have even boasted of holding contradic- 
tory propositions. But where the subject does not imply the 
predicate, there is no self-contradiction, and the opposite of 
any such proposition may be conceived. That things medi- 
ately coinciding, should not immediately coincide, is conceiv- 
able ; for the facts are different ; the difficulty that we feel is 
in contradicting our habitual experience on a matter so very 
familiar and tangible. 

Propositions of avowedly inductive origin may be so strongly 
associated that their opposites are all but impossible to con- 
ceive. It is scarcely in our power to conceive colour without 
extension ; and yet the two are united solely by our experi- 
ence ; they strike the mind through different avenues, and their 
incessant conjunction constitutes a practically indissoluble 



224 DEMONSTRATION— AXIOMS.— NECESSARY TRUTH. 

bond. We should have some difficulty iu conceiving soot 
flakes, particles of dust, and small pieces of paper, falling to 
the ground plumb and swift like a stone. The Greek proverb 
for the impossible was water flowing back to its source. 

The Nature of Axioms. 

7. The fundamental principles of the Deductive Sciences 
are called Axioms. 

Every Deductive Science must begin with certain funda- 
mental assumptions. In Mathematics, and in Logic, these are 
deemed so self-evident, that no express effort is made to 
establish them. In Mechanics, the statement of the Laws of 
Motion is accompanied with a few examples to make them at 
once intelligible and evident. In Chemistry, the Atomic 
Theory is somewhat too far removed from ordinary compre- 
hension to be called a self-evident axiom, albeit the most fun- 
damental assumption contained in the science. 

The requisites of an axiom are, first, that it should be a real 
proposition, and not a definition ; and, secondly, that it should 
be independent of any other principle within the science. 

On the first of these two requirements, we should have to 
reject Euclid's axioms — ' Magnitudes that coincide are equal/ 
and 'The whole is greater than its part/ 

On the second requirement, we must reject, — 

The differences of equals are equal ; 

If equals be added to unequals, the wholes are unequal ; 

If equals be taken from unequals, the remainders are 
unequal ; 

Doubles of equals or of the same are equal ; 

Halves of equals or of the same are equal ; 

Two straight lines cannot be drawn through the same point, 
and parallel to the same straight line, without coinciding. 

It may be useful to give an explicit statement of these 
truths, but as they are all derivable from other axioms 
(together with Definitions), they should be appended to these 
others, as corollaries or inferences. If, in any instance, we set 
up a derivative proposition as an axiom, we break down the 
sole boundary between axioms and the propositions or theorems 
constituting the body of a science. 

8. The only two Axioms of Mathematics, properly so 
called, are, the axiom of 'mediate coincidence/ arid the 
axiom of the ' equality of the sums of equals/ These are 
Inductive truths. 



AXIOMS OF MATHEMATICS. 225 

The excision of Definitions with their corollaries, and of 
Derivative Propositions, leaves only the two axioms now men- 
tioned — * Things equal to the same thing are equal, 1 and ' Tho 
sums of equals are equal.' These are real, and not essential or 
analytic, propositions: and they are ultimate within | 
science. They are two distinct tests of equality, over and 
above the defining test, immediate coincidence. From them, 
together with the definition, all other tests of equality are 
deducible. 

To say that they are Inductive truths, generalizations from 
our experience of the particular facts, is to say that they have 
the same origin as the great mass of our knowledge (not 
deductive). That day and night alternate, that water flows 
downward, that smoke ascends, that plants grow from seed, 
that animals die, that men seek pleasure and eschew pain, — are 
all obtained by a comparison of observed facts ; and this is the 
regular, the usual source of scientific generalities. The burden 
of proof lies upon those that would assign any other source to 
the two axioms named ; some reasons must be given to show 
that they are exceptions to the prevailing rule. 

The chief reasons actually assigned are those already ex- 
amined, their Necessity, and the Inconceivability of their Op- 
posites. As corroborating these, or rather as putting in a 
different shape the supposed difficulty of referring the axioms 
to experience, it is said that the intensity of our conviction that 
4 things equal to the same thing are equal ' is greater than could 
arise from the accumulated comparisons that we have instituted 
on actual things. The considerations that serve to obviate 
what force there is in this objection are the following. 

First, by the law of Belief already explained, every uncon~ 
tradicted experience has, on its side, all the force of our primi- 
tive credulity. The initial believing impetus of the mind errs 
on the side of excess ; and if nothing has happened to check 
it in a particular case, it will be found strong enough for 
anything. 

Secondly, our opportunities of comparing magnitudes are 
numerous and incessant ; they require only the very simplest 
and most accessible instruments. The child, having at com- 
mand, three equal chips of wood, cannot avoid miking, in the 
course of an hour, scores of comparisons that exemplify the 
axiom of mediate equality. 

Thirdly, it is usual to remark, on the mathematical axioms 
generally, that the subjects of them — namely, magnitudes and 
forms — are with the greatest possible ease represented in ima- 



22G DEMONSTRATION.— AXIOMS.— NECESSARY TRUTH. 

crination, so that wc can make numerous ideal experiments, in 
addition to our comparison of actual things in the concrete. 

9. The Axioms of the Syllogism repose upon experience. 

In the form — ' Attributes co-existing with the same attri- 
bute, co-exist/ we have a principle closely resembling Euclid's 
first axiom of Equality ; the character of the evidence for both 
must be the same. Now, so far is this axiom from being an 
absolute and intuitive certainty, that it is erroneous. We may 
illustrate it by a parallel form, 4 Things in contact with the 
same thing are in contact with one another ;' which is plausible 
but fallacious. 

The dictum de omni et vullo cannot be exempted from the 
criterion of experience. It is not intelligible without much 
familiarity with examples of the generalizing process ; and, as, 
in the case of all other first principles, the same knowledge 
that makes it understood, suffices to verify it. 

However expressed, the Axioms of the Syllogism are, in the 
first place, Real Propositions, and not identical statements under 
the so-called Law of Identity, or Self- Consistency. And, in 
the second place, as Real Propositions, they are not intuitively 
suggested to the mind ; they grow up with our experience, and 
if our belief in them seems to outrun experience, the same 
thing happens to all our beliefs. 

10. As regards the Law of Causation, usually included 
among the so-called a priori elements of ourknowledge, there 
is a strong primitive tendency to believe it in a crude form, 
while experience must adapt this belief to the actual facts. 

We have already seen that the primitive tendency of the 
mind is to believe, until checked, that what is now will continue, 
that what is here is the same everywhere. Neither experience 
nor any intellectual faculty creates this impetus ; but experi- 
ence arrests and modifies it, till by degrees it adapts itself to 
the real occurrences. The headlong impulse is curbed in such 
matters as the surrounding temperature, luminosity, and visi- 
ble appearances ; it is left in possession of other matters, as the 
force of gravity. The instinct is important as giving the active 
element of belief; it is perfectly worthless as a guide to the 
things proper to be believed. So far as concerns the authority 
or evidence, for causation, experience is paramount over 
instinct ; apart from experience, the infant would for life be- 
lieve that all the water of the globe is of the temperature of its 
first bath. 



THE UNIFORMITY OF NATURE. 227 

The crude impulse to believe that what is will continue, 
after the shock of many contradictions, is transformed into a 
belief in the uniformity of nature, as represented by the law of 
Causation. 

11. The axiom underlying the axioms of Mathema 
and the axiom of the syllogism, is the axiom of the Uni- 
formity of Nature. 

The consideration of cause and effect brings us face to face 
with the most fundamental assumption of all human know- 
ledge, expressed by such language as * Nature is •Uniform' 
1 the Future will resemble the Past', ' Nature has fixed Laws.* 
This axiom is the common ground of all inference, whether 
avowedly inductive, or induction disguised under the forms of 
deduction. Without this assumption, experience can prove 
nothing. Wo may have found, in ten thousand instances, that 
magnitudes coinciding with the same magnitude also coincide 
when applied to one another ; so far as these instances go, the 
fact is not to be disputed ; the evidence of actual trial is the 
highest we have. But they do not prove that it will happen 
in any untried instance. This must be received without proof; 
it can repose on nothing more fundamental than itself. If we 
seem to offer any proof for it, we merely beg it in another 
shape. (See Appendix D.) 



1 



PART II. 

INDUCTION, 



BOOK IIL 

INDUCTION. 



CHAPTER I. 

MEANING AND SCOPE OF INDUCTION. 

1. Induction is the arriving at General Propositions, by 
means of Observation or Fact. 

In an Induction, there are three essentials: — (1) the result 
must be a proposition — an affirmation of concurrence or non- 
concurrence — as opposed to a Notion: (2) the Proposition 
must be general, or applicable to all cases of a given kind : (3) 
the mechod must be an appeal to observation or Fact. 

(1) By Induction, we arrive at Propositions, — Affirmations 
of coincidence or non -coincidence of distinct properties ; we 
have to do, not with verbal, but with Real Predication. That 
* The boiling temperature destroys animal life,' is an induction 
so far as being a proposition, affirmation, or real predication ; 
there are two distinct facts — ^boiling heat, and destruction of 
animal life — and these two facts are coupled in an affirmation 
of coincidence. 

To this essential of Induction, are opposed the cases where 
what we arrive at is a Notion or Definition. Sometimes we 
are liable to confound the two. This happens when we are 
attending too exclusively to the second characteristic of Induc- 
tion — generality. In the process of defining, we generalize a 
number of individuals, so as to obtain and express their point 
or points of community, which expressed community is a De- 
finition or Notion ; as Heat, Knowledge, Justice. If such 
definitions, or expressed general notions, are absolutely limited 
to one indivisible fact or attribute, they are by that circum- 
stance decisively contrasted with inductions, which always join 



232 MEANING AND SCOPE OF INDUCTION. 

at least two facts or attributes. Thus, the generalized notions 
of length, resistance, whiteness, heat, could not be confounded 
with inductions ; there is clearly absent from these the con- 
joining or coupling of distinct properties. But we have seen 
many instances where a definition expresses a plurality of 
attributes concurring in the same subject, as in all the natural 
kinds — minerals, plants, animals— and in various other things. 
There is no small delicacy in placing the boundary between 
those generalities ending in plural notions, or definitions, and 
proper inductive generalizations. We have to ask whether or 
not the stress is laid on the circumstance of conjunction, 
whether it is made a question — are the properties conjoined 
or not. In definition, the conjunction is tacitly assumed ; in 
induction, it is laid open to question ; it has to he proved or 
disproved, (See p. 292). 

(2) The Propositions established by Induction are general. 
A single individual concurrence, as c the wind is shaking the 
tree,' is in its statement a proposition, but not an induction. 
On such individual statements, we base inductions, but one is 
not enough. If the coincidence recurs, we mark the recur- 
rence ; we are affected by the shock or flash of identity, a very 
important step in our knowledge. If, pursuing the sugges- 
tion, we remark that as often as the wind is high, the trees 
are shaken ; that the two things have concurred within the 
whole course of our observation ; that the same concurrence 
has been uniform in the observation of all other persons 
whose experience we have been informed of,— we are then 
entitled to take a still wider sweep, and to say, ' every time 
that a high wind has been observed, a waving of the trees has 
also been observed.' . 

Still, with all this multitude and uniformity of observations, 
there is no proper Induction. What then remains ? The 
answer is, the extension of the concurrence from the observed 
to the unobserved cases— to the future which has not yet 
come withm observation, to the past before observation began, 
to the remote where there has been no access to observe. This 
is the leap, the hazard of Induction, which is necessary to 
complete the process. Without this leap, our facts are 
barren ; they teach us what has been, after the event ; whereas, 
we want knowledge that shall instruct us before the event* 
tnat shall impart what we have no means of observing. A 
complete induction, then, is a generalization that shall express 
wnat is conjoined everywhere, and at all times, superseding 
tor ever the labour of fresh observation. 



IMPROPER INDUCTIONS. 

We thus contrast Induction with that species of 'Induc- 
tions improperly so called/ where a general statement merely 
sums up the observed particulars. 

If, after observing that each one of the planets shines by the 
sun's light, we affirm that ' all the planets shine by the sun's 
light/ we make a general proposition to appearance, but it 
falls short of an induction in the full sense of the term. The 
general statement is merely another way of expressing the par- 
ticulars ; it does not advance beyond them. Uut without such 
an advance there is no real inference, no march of information, 
no addition to our knowledge. Induction is the instrument of 
multiplying and extending knowledge ; it teaches us how, 
from a few facts observed, to affirm a great many that have 
not been observed. If, from the observation of the planets 
now discovered, we make an assertion respecting all that have 
yet to be discovered, we make the leap implied in rear or 
inductive inference. If the assertion had been made when 
only six planets were known, actual observation would have 
been the guarantee for those six, induction for the remaining 
hundred or upwards* 

Sc the proposition ' all animals have a nervous system ' is 
an induction only when affirmed on the observation of a part 
of the animal species. If the representatives of every species 
had been examined before the statement was made, the pro- 
position would be proved by observation, and not by induction; 
the generality would be merely a literal repetition or summary 
of the particulars. 

This kind of improper induction is assumed in the attempt, made 
first by Aristotle and repeated by others, to bring Induction under 
the syllogism. Induction 'is defined by Aristotle, "proving the 
major term of the middle by means of the minor ;" in which 
definition, the expressions major, middle, and minor, are used 
relatively to their extension, to designate respectively the attribute 
proved, the constituted species of which it is proved, and the 
aggregate of individuals by which the species is constituted.' 
(Manser s Aldrich, Note G.). Thus— 

X, Y, Z, (minor) are B (major), 
X, Y, Z, are all A (middle). 
All A is B. 

This has the appearance, but only the appearance of a syllogism 
in the Third Figure. It is liable to the criticism already made 
upon syllogisms with two singular premises. It is not a syllogism 
at all, in any correct sense, but a mere process of equivalence. The 
two premises can be summed in one, by verbal or grammatical 
condensation ; and when that has been done, the conclusion is a 
mere repetition of part of the meaning of the combined statement. 



334 MEANING AND SCOPE OF INDUCTION. 

A more ambitious form of the Inductive Syllogism is given by 
Aldrich and Whately, which trenches on Induction proper. 

The magnets that I have observed, together with those that J 

have not observed, attract iron. 
These magnets are all magnets. 
All magnets attract iron. 

The major here obviously assumes the very point to be estab- 
lished, and makes the inductive leap. No formal logician is entitled 
to lay down a premise of this nature. The process altogether 
transcends syllogism or formal logic. 

In no sense is the Inductive {Syllogism an admissible logical 
form. 

A truly inductive Proposition may be but a narrow genera- 
lity. That 'the breeze always spreads the royal flag hoisted 
at Windsor Castle ' is a proper induction ; it covers the unseen 
and the future as well as the seen. The still wider induction, 
* the breeze spreads all the flags of all nations/ is not more 
essentially inductive, although of more value as knowledge. 

(3) An Inductive Proposition is based on the observation 
of facts. Many true propositions, instead of being based on 
a direct appeal to observation, are derived from other propo- 
sitions ; such are, with a few exceptions, the propositions of 
Mathematics, and many truths in all the other sciences. In 
this view, Induction is contrasted with Deduction. Induction 
is necessarily the prior source of truths ; the Deductive pro- 
positions are obtained from Inductions. We must commence 
with observation of fact, and thence rise to Inductive gene- 
ralities, before we can proceed downwards in the way of 
deduction. 

By the use of our observing faculties for the object world, 
and of self-consciousness for the mind, we not merely obtain 
our notions of things — stars, mountains, trees, men, pleasures 
— but also discern the conjunctions or connexions of things. 
A single conjunction excites little notice, but an iterated con- 
junction awakens our feeling of identity ; we attend to the 
circumstance, and watch for the recurrence. If, in the midst of 
fluctuation, some one couple of things is found always associ- 
ated, we state the fact to ourselves as a natural conjunction, a 
law of nature ; and the statement is an inductive proposition. 
A meteor flashing along the sky is an isolated circumstance ; 
we term it casual or accidental. The recurrence of a stream 
of meteors year after year, in the same month, is a coincidence, 
which we elevate into an induction, affirming it for the future 
as well as for the past. 

The semblance of Induction is put on by certain operations 

\ 



INDUCTION AND DEDUCTION CONFOUNDED. 

purely Deductive. Of these Inductions improperly so c 
two forms may be mentioned. 

First. There is a certain likeness to Induction in tho demon- 
strations of Euclid; which are each made upon at) exemplary 
diagram, and thence extended to all similar instances, by what 
is termed parity of reasoning. 

When Euclid proves that the angles at the base of an isos- 
celes triangle are equal, he proves it upon a single diagram, 
and rests the general proposition upon the circumstance that 
the same result would be arrived at in every other case of tho 
same sort. The resemblance to Induction lies in extending 
what is found in one instance to all other instances. Yet the 
resemblance fails on vital points. 

In reality, such truths are not established by measuring the 
particular diagram, and recording that measure as an observed 
tact, to be taken with other facts similarly observed, in mak- 
ing up a general rule ; as if we were, by means of an induction 
from the pyramids, to lay down a general law of pyramid ical 
structure. The only use mada of the figure is to provide a 
concrete reference in applying the general language of tho 
demonstration. One triangle is as good as another for the 
purpose. We expressly omit from the reasoning all reference 
to the size of the triangle, to it3 material, to the size of the 
angle included by the two equal sides ; consequently, our 
proof is independent of any one of these elements, and holds 
under all variations of each. The demonstration is to the 
effect that, quoad isosceles triangle, the affirmation is true ; it 
is a perfectly general truth. The expression, ' the same might 
be proved of any other isosceles triangle,' would be idle and 
superfluous; the fact is already proved of every such triangle. 

Secondly. The term Induction has been improperly applied 
to discoveries of identification to establish a minor — a purely 
deductive operation. 

When Kepler, after comparing a great many positions of 
Mars, came to the conclusion that all these places lay in an 
ellipse of certain dimensions, he made an advance from tho 
known to the unknown, which is one criterion of induction. 
Without any farther observations, it was possible to assign 
the place of the planet at any moment of time throughout 
the entire circuit. Yet, notwithstanding this remarkable 
peculiarity, the case is not an induction. It i?, in fact, a 
deduction. We might term it a discovery of identification to 
establish a minor. 

Supposing that, in the time of Kepler, the geometrical pro- 



236 MEANING AND SCOPE OF INDUCTION. 

positions of the ellipse had been still undiscovered, he could 
not have established his law, nor applied it to fill in the inter- 
mediate places of the planet. What he really discovered was 
an identity between the scries of observed positions of Mars 
and the path of an ellipse with the snn in the focns. It was 
by the help of the known properties of the ellipse that he made 
this identity. The identity once established, any or all of the 
propositions of the ellipse could be applied to the orbit of 
Mars, and by these the orbit conld be as it were drawn, so as 
to show the successive positions of Mars as he described his 
circuit. There could have been no inference from places 
observed, to places unobserved, except through the application 
of those laws respecting the ellipse, which had been dis- 
covered by the Greek geometers. The propositions of the 
ellipse supplied the major premise of the reasoning. Kepler's 
observations supplied the minor premise ; they showed that 
the places of Mars coincided with the places in an ellipse ; 
whereupon whatever was true of the ellipse was true of the 
orbit of Mars. 

Similar instances of discoveries of Deduction could be cited. 
When after the inductive establishment of the laws of 
magnetism upon Iron, other substances were discovered to 
be magnetic as Nickel, Cobalt, Manganese, Chromium, &c, 
the magnetic laws were forthwith transferred deductively to 
these bodies. Franklin's great discovery of the identity of 
lightning and electricity, enabled all the previously ascertained 
facts regarding electricity to be applied to the atmospheric 
charge. 

In contrast to the law of the elliptic orbits, we may quote 
Kepler's third law— the relation of the periodic times to the 
mean distances, an induction in the proper sense of the word. 
There is still a mathematical element present, but that element 
is not the major proposition, to which Kepler supplied a minor. 
The numerical ratio merely expresses the point of concurrence 
of the particulars observed, it being the nature of that con- 
currence to be numerical. The basis of the induction was the 
agreement of the six planets in the numerical ratio ; and the 
induction was brought out in its real character when new 
planets were discovered and the law applied to them at once, 
and before there was time to observe the fact in each indivi- 
dual case. 

Of a similar nature to Kepler's third law Is the law of the 
refraction of light, a proper induction set in mathematical lan- 
guage. From a number of positions of the incident and re- 



■ 



FUNDAMENTAL INDUCTIVE METHOD. 237 



fracted rays of light in various substances, Sncll found that 
the relation of the two could be expressed by a definite 
numerical proportion of the sines of the angles, (he proportion 
being constant for the same transparent medium. He had 
observed the relation in a number of cases, and he inductively 
affirmed it in all. 

In like manner the establishment of the law of gravitation 
was an induction numerically expressed. 

2. The sole method of attaining Inductive truths being 
the observation and the comparison of particulars, the sole 
evidence for such truths is Universal Agreement. 

A permanent or uniform concurrence can be established, in 
the last resort, only by the observation of its uniformity. That 
unsupported bodies fall to the ground, is a conjunction sug- 
gested by the observation of mankind, and proved by the 
unanimity of all observers in all times and places. What is 
found true, wherever we have been able to carry our observa- 
tions, is to be accepted as universally true, until exceptions are 
discovered. This is to apply the Universal Postulate, the 
primary assumption at the root of all knowledge beyond the 
present— that what has never been contradicted (after sufficient 
search) is to be received as true. 

Through this method alone — of Universal Agreement in de- 
tail — can our most general and fundamental truths be dis~ 
covered and proved. It is the only proper Inductive Method. 
By it are established the Axioms of Mathematics, the Axioms 
of the Syllogism, the Law of Gravity, the Law of Causation or 
of Conservation. Likewise on it we depend for the proof of 
all uniformities that, although not ultimate, are for the time 
unresolved into higher uniformities ; or what are termed Empi- 
rical Laws. 



CHAPTER IL 

THE GEOUND OF INDUCTION---UNIFOKMITY OF 
NATURE -LAWS OF NATURE. 

1. As Induction proper infers from the known to the 
unknown ; it assumes that, under certain circumstances 
(to be specified), what has been will be. The same thing 
is otherwise expressed by affirming that Nature is Uni- 
form ; that there are Laws of Nature. 

This great foundation of all possible inference is stated in 
many forms of language. ' Nature repeats itself/ * the future 
will resemble the past/ ' the absent is like the present/ ' the 
Universe is governed by Laws/ In one great department, it 
is named Causation, or the Law of Cause and Effect. 

The principle is put in another light by the remark of Mr. 
Mill that the Uniformity of Nature is the ultimate major premise 
of every inductive inference. To prove that the present 
generation of men will die, we may construct a syllogism 
thus : — major — what has been in the past will continue 
(under given circumstances) ; minor — men have died in the 
past ; conclusion — men will continue to die. 

Nature is not uniform in all things. One day agrees with 
another in part, and differs in part. Human beings are 
born with a certain amount of uniformity, and also with 
a certain amount of difference. The law of uniformity, there- 
fore, needs to be limited and qualified. 

2. The course of the world is not a Uniformity, but 
Uniformities, There are departments of uniformity, which 
are radically distinct. 

The most pointed illustration of this statement is the 
Classification of the Sciences. Although, in early ages, men's 
minds were strongly prepossessed with a supposed Unity of 
Nature, we now recognize a plurality of distinct kinds of 
phenomena, each kind having its own separate principles or 
laws. Thus, the facts and principles of Number are studied 
apart from the facts and principles of Life. 



LAWS OF NATURE, 

The phrase ' Laws of Nature ' may bo understood io imply 
(1) that Nature is uniform, and (2) that this uniformity is a 
plurality and not a unity. There are separate departm- 
each with its own uniformities or laws. That unsupported 
bodies fall to the ground, that fire is quenched by water, that 
men pursue pleasure — are said to be laws of nature ; they are, 
however, generically different laws, and are distributed under 
distinct branches or departments of Science or Knowledge. 

The word 'Law ' is a metaphor taken from human society, 
where it supposes the relationship named authority and obedi- 
ence. Seeing that in all well-constituted societies, the decrees 
emanating from the sovereign authority are alike binding upoxi 
all citizeus, in all times and places, they have the characteristic 
of uniformity ; and it is on this characteristic alone, that i law ' 
can be employed to signify the order of the natural world. 
The full definition of a law is inapplicable to physical sequences. 
The likeness fails in the essential point. In human authority, 
a certain beneficial result is aimed at by rules of conduct on 
the part of the subjects of the state ; which conduct is enforced 
by a penalty or punishment ; and the penalty is directed with 
precision upon the wrong doer. In the order of the world, 
on the contrary, a man conforming to the physical sequences 
is safe, whatever be the extent of his violations of moral law. 
Night exposure may be more injurious to the policeman than 
to the thief; immunity is pnrchased not by virtuous conduct 
as regards others, but by prudential care as regards self. 

3. The term 'Law of Nature' is sometimes used in a 
more restricted sense, to express the highest generalities, 
or ultimate uniformities of nature. 

There being a constant wish to discover, not merely laws 
that shall be true, but laws of the highest and most command- 
ing generality, such laws are more emphatically termed 
1 The Laws of Nature' — the most centralized and all-compre- 
hending expressions of the order of nature. This more 
imposing character appears to belong to the law of Gravity, 
and to the principle named ' The Conservation of Force.' 

4. As regards Logical Method, the general Uniformity 
of nature may be distributed under three branches, already 
expressed in the ultimate classification of Propositions — 
Co-existence (as Co-inherence of Attributes), Causation, 
and Equality. 

The three great relationships found capable of embracing 



240 THE GROUND OF INDUCTION. 

nil propositions were stated to be (1) Co-existence, (2) 
Sequence, (3) Equality and Inequality (Number and Quan- 
tity). Under Co-existence was included Order in Place, and 
Omnheking Attributes; the first—Order in Place, being 
resolvable into laws of Quantity. Under Sequence or Succes- 
sion was included Order in Time and Causation; the first-named 
Being also a purely numerical relationship. The third rela- 
tionship, Equality and Inequality, is the basis of Mathematics, 
the science of Quvntity and Number. 

Thus the three distinct heads of scientific investigation, 
comprising all the uniformities or laws of nature, are Unifor- 
mities of Co-existence, Uniformities of Succession (Causation), 
Uniformities of Equality and Inequality. These are the three 
cases that Induction has to deal with. 

In the actual working of Induction, we find it to be almost 
entirely absorbed with the second head — Causation. 

Besides that there are very few general laws of pure Co- 
existence, Causation is singular in providing a comprehensive 
Uniformity, which may be appealed to deductively, for all 
cases. The uniformities of Co-existence (independent of 
Causation) can be proved only piece-meal; each stands on its 
own evidence of observation in the detail ; no one assists us 
to prove another. There is thus a blankness of resources 
in regard to the proper laws of Co-existence ; their Logic is 
speedily exhausted. 

The same defect, strange as it may sound, attaches to the 
uniformities of Quantity— based on the relations of Equality 
and Inequality. The certainty of the mathematical axioms is 
a certainty due to their easy and thorough verification one by 
one ; not to their falling under any uniformity more compre- 
hensive than themselves. It is by • Agreement through all 
Nature ' that we prove that * Things equal to the same thing 
are equal ; *■ having found this fact always true, never false, 
we extend it, by the Inductive hazard, to all cases whatsoever. 
We repeat the operation upon the other great axiom — ' The 
sums of equals are equal/ We must proceed, in the same 
method of detail, to all other axioms— as the dictum of the 
syllogism, the axiom a fortiori, &c. 

The extended machinery of Inductive research, constituting 
the Logic or Method of Induction, is thus nearly confined to 
Causation. The greatest resources for eliminating accidental 
accompaniments and for seizing the real concomitances of 
facts— the so-called * Experimental Methods' — have their full 
application only to Cause and Effect. 



CHAPTER in. 

INDUCTION OF CO-EXISTENCE. 

1. Of Uniformities of Co-existence, a very large num- 
ber may be traced to Causation. It remains to be seen 
whether there be any not so traceable. 

The numerous Co-existences of Order in Place, or the dis- 
tribution and arrangements of material objects throughout the 
Universe, are all the results of causation, starting from some 
prior arrangements. The distribution of sea and land, the 
stratification of the earth's crust, the existence of an atmos- 
phere, the distribution of the materials of the globe generally, 
— are the result of natural agencies or forces, operating npon 
prior arrangements. Salt is found in the ocean, because the 
water has dissolved all accessible portions of it. The heavy 
metals are found in deep rocks in cod sequence of their weisrht ; 
the corrosible and combining metals occur in combination ; 
and those that are reluctant to combine, occur nearly pure, as 
Platinum and Gold. 

There are thus no independent laws of co-existence to be 
found among uniformities of Order in Place. We must seek 
for them, if there be any such, among Co-inhering Attributes. 
It is possible that attributes or properties not connected as cause 
and effect, may yet be conjoined uniformly through all nature. 
If so, they are likely to be found among the natural kinds — 
Minerals, Plants, Animals. The conjunction of body and 
mind in man, and in the animals, is to all appearance such a 
case as we are in quest of. 

2. It is the special peculiarity of the Natural Kinds to 
combine many attributes in unity of subject. In them we 
have the chief exemplification of co-inhering attributes ; 
and they seem to furnish uniformities of co-existence. 

Thus Gold unites a certain specific gravity (19.3), crystal- 
lization (cubical), tenacity, fusibility (melting point, 1200° C), 
colour and lustre (yellow), electrical conduction, atomic weight 
(196), combining properties (acted on by aqua regia). These 
are eight leading attributes that concur in every piece of gold ; 



2±2 INDUCTION OF CO-EXISTENCE. 

and unless we see our way to deriving some of them from 
Others, we must pronounce them essentia?, essential or defining 
attributes of gold. There is a co-existence, or co-inherence of 
these eight facts, with others, in the object named gold. 

To appearance there is here a uniformity of co-existence. 
No specimen of gold is devoid of any one of the eight proper- 
ties. Properly speaking, however, this is merely affirming an 
identical proposition. Should there occur a specimen wanting 
in one, two, or three of the eight, we should say not that a law 
of co-existence was infringed, but that a different substance 
Was produced. If these be the essential attributes of gold — the 
meaning or connotation of the name, then, on the failure of any 
one or more, the name w r ould cease to be applied, the substance 
would not be ranked as gold, it would be classed as a new and 
distinct substance. Gold with the specific gravity of 9, or 
with a silvery colour, or with a liability to corrode, would not 
be gold, it would be treated as a different materia), a distinct 
grouping or aggregate of powers and properties. If there be 
any one of the now enumerated properties of gold that w T e 
could see changed and yet keep up the designation gold, that 
property is declared not to be the essence, but a concomitant 
of gold. A proper inductive enquiry w T onld hold in such a case. 

3. For a Law or Uniformity of Co-existence, properly 
so called, we must refer to examples, if such there be, 
where two or more independent properties are conjoined 
through all nature, or in all substances where one of them 
occurs. 

We must search among the properties of kinds — mineral, 
vegetable, and animal, for some that are coupled throughout 
every species, and under every variety of aggregation. For 
example, could we find a certain crystalline form regularly 
conjoined with certain chemical characters, not in one sub- 
stance only, but in all substances possessing that crystal- 
lization, — this would be a proper law or uniformity of co-exist- 
ence. There would still remain a question, often difficult to 
settle — whether, on the one hand, the two are mutually im- 
plicated properties, or, on the other hand, whether they are 
connected by cause and effect. 

To detect such uniformities of general co-existence, among 
ttie essential properties of mineral bodies, whether simple or 
cc mpound, is a proper object of scientific enquiry. Nor has 
it been neglected by physical enquirers. The following are 
the leading examples obtained up to the present time. 



LAWS OF CO-EXISTENCE. 

(1) A law has been discovered connecting Atomic Weight 
and Specific Heat by an inverse proportion. l\>r equal 
weights of the simple bodies, the atomic weight, multiplied by 
a number expressing the specific heat, gives a nearly uniform 
product Thus, for sulphur, the atomic weight (32), multi- 
plied by the specific beat (0.1776), gives 5.08; the atomic 
weight of platinum (197), multiplied by its specific heat, 
(0.0o24), gives 6,38. The products for all the elements are 
near the constant number 6. 

(2) A law obtains between the Specific Gravity of substances 
in the gaseous state and the Atomic Weights. Thus, the specific 
gravity of oxygen is 16, its atomic weight 16; hydrogen, 
specific gravity 1, atomic weight 1 ; phosphorus, specific 
gravity 62, atomic weight 31 (the relation here is 2 to 1) ; 
steam, specific gravity 9, atomic weight 18 (relation of 1 to 2). 
The relationship of the two numbers is thus, in some instances 
equality ; in other instances, the one is a multiple of the 
other. The law is one of importance in ascertaining atomic 
weights. 

With an exception to be noticed presently, these are perhaps 
the two most widely-operating laws, as yet discovered, whereby 
two distinct properties are conjoined throughout substances 
generally. There are various laws of narrower range, as, for 
example, Andrews's laws of the heat of combination of the 
metals. 

4. A peculiar importance belongs to the law of universal 
co-existence uniting the two properties — Inertia and 
Gravity. These properties are co-existent through all 
matter and proportionate in their amount. 

Inertia, the defining attribute of matter, means both resist- 
ance to movement, and force when moved. It is totally dis- 
tinct from gravity. A body rolled on a level surface shows its 
inertia; so also do two weights equipoised, as in the beautiful 
experiments of Attwood. Now, all inert matter gravitates ; 
and the force of gravitation is proportional to the inertia. 
Equal weights, (which are the estimate of gravity), are equally 
resisting to a horizontal impulse (the measure of inertia) or to 
a vertical impulse in the balanced condition. 

It cannot be maintained that these properties are mutually 
implicated. We can easily suppose matter (considered as 
inert) without the property of distant mutual attraction, or 
gravitation ; this last property may be fairly viewed as added 
to, or superinduced upon mere inertia. Nor can we call the 



Qj.4 INDUCTION OF CO-EXISTENCE. 

two cither cause and effect, or effects of a common cause ; onr 
knowledge does not entitle us to make either supposition. Wo 
can prove cause and effect only by exhibiting first a cause, 
and then an effect flowing from it. Here the two facts or 
properties are inseparable. 

There is no other equally unambiguous instance of a law of 
universal co-existence. The examples above quoted with 
reference to three properties — specific gravity in the gaseous 
state, atomic weight, and specific heat — may, for anything we 
know, be mutually implicated, or related as cause and effect. 
K we understood more thoroughly the ultimate arrangement 
of the atoms of bodies, and their intestine motions, we might 
not improbably find that some one fundamental property was 
at the foundation of all the three ; — a real essence, of which 
these are but prop via. As regards many of the minor laws, 
the existence of either implication or causation is more than a 
mere surmise. 

Under such circumstances we are entitled to conclude that 
uniformities of general co-existence are very rare. The pre- 
sumption or probability (although not the certainty) in every 
new case of uniformity is that it is a case of causation and not 
of co-existence. Thus, the conjunction of Mind and Body may 
be a co-existence independent of causation, like inertia and 
gravity ; but it may also follow the more prevailing type, and 
be a case of cause and effect. Which is cause and which 
effect, or whether they are effects of a common cause, may be 
open to dispute. 

5. The only proof of Uniformities of Go-existence not 
known to depend en causation, is uncontradicted Agree- 
ment through all nature. 

This is the proof of the Law of Causation itself. Now any 
uniformity not coming under causation must stand on its 
own independent evidence; and this evidence is uniform 
agreement throughout the whole compass of observation. 
We must find it true in all times, all places, and all circum- 
stances ; and provided our search has been so extensive, that if 
there were any exceptions we should light upon them, and no 
exceptions have been found, we are entitled to declare it a law 
of all nature. 

The coincidence of gravity with inertia has been proved over 
the entire globe ; it applies undoubtedly to the solar system ; 
and by very strong aualogy to the distant stars. This, there- 
fore, may be held to be an established uniformity of co-existence. 



r 



CONCOMITANT PKOPERTIES OF KINDS. 



The alliance of mind with a bodily mechanism cxt< 
throughout the whole of animal life, past and present 

The co-existences above mentioned regarding the propyl 
of gaseous specific gravity, atomic weight, and specific heat, 
have to be verified by the method of Agreement throughout all 
bodies. We cannot, as in cause and effect, presume from a 
small number to all tho rest. 

6. The special coincidences making up the Natural 
Kinds must also be verified by Agreement over the whole 
field of instances. 

"We have already remarked that an exception to a kind, 
arising from the failure of an essential property, would not be 
the infringement of a uniformity, but the setting up of a new 
kind. The only case for proving a co-existence would be the 
case of concomitant properties, or those not adopted into the 
essence or connotation of the kind. Of such a character is the 
blackness of the crow, the whiteness of the swan, and varia- 
tions of colour generally ; a point seldom treated as essential, 
whether in minerals, plants, or animals. Now the sole proof 
that ' every crow is black/ is observation through all Nature ; 
so long as no other colour is seen, we affirm the general pro- 
position ; the occurrence of various albinos has disproved the 
generality, and reduced it to an approximate generalization, of 
a very high order of probability. 



CHAPTER IY. 
LAW OF CAUSATION. 

1 . The Uniformities of Succession presented in nature 
are subject to one great uniformity — the law of Causation. 

The law may be expressed thus :— In every change, there 
is a uniformity of connexion between the antecedents and the 
consequents. 

No single expression sums up all that is implied in Cause 
and Effect. When it is haid, ' Every effect has a cause, and 
every cause an efiect, and that the sequence is regular,^ the 
same causes being always followed by the same effects,' the 



2£j LAW OF CAUSATION. 

proposition is an identical statement; the word ' Cause' means 
what brings about i\n effect; and the word 'Effect,' what 
follows from a cause. To avoid this objection, we may state 
the law as follows : — 'Every event that happens is definitely 
and uniformly connected with some prior event, or events, 
which happening, it happens; and which failing, it fails.' 
The kindling of a fire follows regularly on the prior events of 
making a heap of combustibles and applying a light. 

A law is more sharply stated by help of its denials. Causa- 
tion denies two things. First, it denies pure spontaneity of 
commencement. If the law is true, no change arises out of 
vacuity or stillness ; there must be some prior event, change, 
or movement, as a sine qua non of the occurrence of any new 
event. A fire never bursts out without some commencing 
circumstance, in the shape of movement, change, or activity. 

Secondly. The law denies that events follow one another 
irregularly, indiscriminately, or capriciously. The same cir- 
cumstances that make a fire burst out to-day, will, if repeated, 
make it burst out to-morrow, or at any future time. The 
same pain, in the same circumstances, does not at one time 
repel, and at another, attract and allure us. In short, the 
law is the statement of uniformity in the Succession of events. 

2. In Causation, the same cause always produces the 
same effect ; but the converse does not hold ; the same 
effect is not always produced by the same cause. There 
may be Plurality of Causes. 

A severe blow on a man's head will always cause death : 
Lut death is not always caused by a blow on the head. There 
are many causes of motion ; and the presence of any one in 
the proper circumstances, will always be followed by motion. 

This is an important limitation of the law, and has to be 
kept in view in the investigation of causes. If a change has 
occunel, there must have been a previous change, or ante- 
cedent fact, but not necessarily one particular antecedent. 

3. The Plurality of Causes is subject to uniformity in 
two respects : (1) the number of causes is fixed ; (2) the 
character of each is as definite as if it were the sole cause. 

The causes of death may be numerous, but they are all 
fixed and knowabh ; and, when known, may be counted on 
with certainty and precision. The fact of plurality renders 
the causation of an event ambiguous; there may be several 
a.tcmative airtecsisnts. Yet, these antecedents being, once 



PRACTICAL ASPECT OF CASSATION. g 1 1 

for all, exhaustively known, we are sure that one of them is 
the operative circumstance in the case before u 

It will be pointed out afterwards that plurality of causes is 
more an incident of our imperfect knowledge than a (act in 
the nature of things. As knowledge extends, we find k 
plurality. The-numerous apparent eauses of motion are differ- 
ent only in superficial appearance ; they are all OLe at bottom, 

4. Causation may be viewed under three different aspects. 

(1) The first may be called the practical and popular ftepeot 
— a partial view suited to the ordinary emergencies of life. 
Under this aspect, the cause is some one circumstance or 
condition demanding our solicitude, as being precarious. 
Thus, when the soldier, on the eve of an engagement, is urged 
to keep his powder dry, this is not the whole cause of his 
hitting the enemy ; it is the circumstance that happens to be 
in peril at the time. 

(2) The second aspect is the Scientific or complete view of 
Causation. Under this view, all the conditions or antecedent 
circumstances are fully enumerated. 

(3) A third aspect is Causation viewed as embracing the 
modern generalization, entitled the Conservation or Correlation 
of Force. 

CAUSATION PEACTICALLY VIEWED. 

5. In common lan^ua^e, the Cause of an event is some 
one circumstance selected from the assemblage of condi- 
tions, as being practically the turning point at the moment. 

A man slips his foot on a ladder, falls, and is killed. The 
cause of the fatality is said to be the slipping ; for if this one 
circumstance had been prevented, the effect would not have 
happened. Yet, in order to the result, many other conditions 
were necessary : — the weight of the body (gravity ), the height 
of the position (a certain collocation), the fragility of the human 
frame. Yet, for practical purposes, we leave out of sight at 
the moment all the elements that are independent of us and 
secure, taking notice only of s\ hat is in our power and needs our 
attention. By a common ellipsis, all arrangements that are 
fixed and settled, are passed over in silence. We presume 
on the forces of heat and gravity, and devote our care to the 
choice and shaping of the materials whereby these forces may 
be made to work out our ends. 

When we speak of food as the cause of animal strength, we 



24S LAW OF CAUSATION. 

suppose a healthy constitution, able to digest and assimi- 
late it. But, in this particular case, mankind long erred in 
iguorantly suppressing a condition no less essential than 
food, namely, the oxygen of the atmosphere — the aerial 
element of our food.* 

Language is adapted principally to this mode of viewing 
causation. In the distinction of agent and thing acted on, 
which pervades the whole of grammar, and gives the character 
to the active verb, there is an arbitrary selection of one circum- 
stance as cause, other equally indispensable circumstances being 
overlooked. A prize ox is reared in a breed of cattle ; the 
breeder is by courtesy styled the cause or agent ; but his activity 
is only a single, although indispensable circumstance. A teacher 
instructs a pupil, and is credited as the cause or author of the 
pupil's knowledge. A still more glaring ellipsis is practised 
in attributing the issue of a war to the commander-in-chief; 
as when we speak of the conquests of Alexander or Caesar. 
4 The monk that shook the world ' is rhetoric for the agency of 
Luther. 

The first attempt at a precise analysis of Causation was made by 
Aristotle. He enumerates four kinds of Causes. — the material, the 
formal, the efficient, and the final. The material cause is literally 
the matter used in any construction; marble or bronze is the 
material of a statue. The formal cause is the form, type, or 
pattern in the mind of the workman ; as, the idea or design con- 
ceived by the statuary. The formal cause of a building is the 
architect's plan. The efficient cause is the power acting to produce 
the work, the manual energy and skill of the workman, or the 
mechanical prime mover, whether human power, wind, water, or 
steam. The final cause is the end, or motive on whose account the 
work is produced — the subsistence, profit, or pleasure of the 
artificer. 

Aristotle gives the instance of a physician curing himself, as 
combining all the four causes in one subject. 

* Whenever the existence or safety of anything depends upon a sum or 
system of contrivances adapted to a common end — which, together, are 
conditions necessary for its preservation— then the destruction, disturbance, 
or removal of one of these contrivances — the failure of any part of this 
composite system of safeguards — is considered as the cause of the ruin of 
the whole. For example, if the action of any one of the functions or organs 
necessary to human life is stopped, life is extinguished, and the circum- 
stance producing that effect is said to be the cause of death. So, if a ship 
springs a leak and sinks, or if an army is surprised through the absence of 
a sentinel from his post— the springing of the leak, and the absence of the 
sentinel, is said to be the cause of the loss of the ship and the surprise of 
the army. The language by which such an effect is commonly ascribed to 
a merely negative cause is elliptical. (G. C. Lewis). 






SCIENTIFIC CAUSATION. 



This analysis is obviously taken from human industry, wbich 
contains the several circumstances mentioned. It throws no light 
upon causation in the order of nature; while the attemi 
express natural phenomena according to such a scheme, ha\ 
to distortions and unmeaning conceptions. 

The iirst and second causes give the celebrated distinction of 
Matter and Form, which pervades the whole of Aristotle's philo- 
sophy. The third, the Efficient, has continued in the language of 
science; a better designation for the meaning is Prime Mover, or 
Moving Power. The fourth, the Final cause, is more perspicu- 
ously expressed by Motive, End, Intention, Purpose, Object or 
Design ; it applies to nature only as personitied, or as the work of 
a personality. 

SCIENTIFIC CAUSATION. 

6. In scientific investigations, the Cause must be regarded 
as the entire aggregate of conditions or circumstances re- 
quisite to the ett'ect. 

All the conditions suppressed by the practical man are 
brought back by the scientific man in a full statement of the 
cause. If any are omitted, it is because they are so obvious 
that no person could overlook them. There is a legitimate 
ellipsis of expression, even in the scientific enumeration of con- 
ditions. 

The cause of the inundations of the Nile would be described 
as (1} the fall of moisture as snow on the lofty mountains of 
Africa where the Nile has its source ; (2) the melting of this 
snow by the summer heat. Gravity, the laws of heat, the con- 
stitution of water, are all a part of the cause, and if not men- 
tioned, are supposed to be fully present to the mind of the 
hearer. 

The growth of plants is a complicated causation. There 
must concur, the properties of the germ, the contact with the 
soil, air, water, saline bodies in the soil, heat, light, &c. 
The agriculturist thinks only of a select number of these — the 
seed, the quality of the soil, moisture, and heat ; the vegetable 
physiologist brings into view the physical, chemical, and vital 
agencies, which are the causes of the phenomenon in the final 
analysis. 

The cause of vision is summarily given as light entering the 
lenses of the eye. The full enumeration of the circumstances 
would include the optical action of the lenses, the physiology 
of the coats of the eye, and of the nerves and brain ; and 
finally, the link associating a certain activity of the brain with 
& feeling: in the mind. 






250 I^ w 0F CAUSATION. 

Tbo cause of the Reformation was Luther's preaching against 
the sale of indulgences, concurring with the administration of | 
the church, and the state of men's minds at the time.^ 

In speaking of antecedents of the French Revolution, it is 
customary to°use the plural— Causes ; signifying that a union 
of many circumstances or conditions was involved. In the 
enumeration of Alison, no less than sixteen causes are given. 

Gibbon attributes the rapid growth of Christianity to one 
primary cause, namely, the convincing evidence of the doctrine, 
and of the ruling providence of its author ; and to five aiding 
secondary causes, 'which assisted in producing the effect, viz.: 
1, the inflexible zeal of the early Christians; 2, the doctrine 
of a future life, as held by the Christian Church ; 3, the mira- 
culous powers ascribed to the primitive church ; 4, the pure 
and austere morals of the Christians ; 5, the union and 
discipline of the Christian republic.' 

The conditions of phenomena include negative as well as 
positive circumstances ; the absence of hindrances to the 
operation of the agents concerned. The sun is the cause of 
vision, provided he is not screened, provided the subject is not 
asleep or blind. It is usual to suppress the mention of all 
such hindrances, if they are really absent. 

7. The suppressing of essential conditions is a common 
fallacy of Causation. 

When, in the statement of a cause, there is not merely an 
ellipsis of understood circumstances, but an omission of some 
essential fact, the consequence is positive error. 

When the healthy effect of residence at a medicinal spa is 
attributed exclusively to the operation of the waters, there is 
a fallacy of causation ; the whole circumstances and situation 
being the cause. 

This is a common form of Inductive fallacy, and prevails in 
all the complicated sciences, as Politics and Medicine. 

CAUSATION AS CONSERVATION OF FORCE OR ENERGY. 

8. A great advance, in the mode of viewing Causation, 
is made by the modern discovery of the law named ' Cor- 
relation of Force/ or ' Conservation of Energy.' 

The great generalization of recent times, variously designated 
the Conservation, Persistence, Correlation, Convertibility, 
Equivalence, Indestructibility of Energy, is the highest expres- 
sion of Cause and Effect. In every instance of causation, there 






LAW OF CONSERVATION. 



is a putting forth of force in given circumstances, and the law 
in question states exactly what becomes of the force, and is 
I often the sufficing explanation of the special phenomena, M 

(well as the embodiment of nature's uniformity in 
Statement of the Lain of Conservation. 
9. Force, Energy, Moving Power, or Work Pfwqr, is 
embodied in various forms, all mutually convertible at a 
definite (fixed) rate. The extinction of energy in one form 
is accompanied by the creation of energy in another form : 
in the transmutation work is said to be done, and no force 
is absolutely lost. 

(1) Matter in motion is Force manifested as actual, apparent, 
or kinetic energy; but the modes of motion may be very 
various. We are most familiar with that of mechanical 
energy, as in the case of a flying-ball, a water stream, or the 
wind. There is, however, reason to believe that the forces 
named heat, light, and electricity, consist in minute move- 
ments of material particles. 

Matter in position corresponds to a possible production of 
power ; or the configuration of a material system corresponds, 
in virtue of the mutual action of its parts, to a definite amount 
of possible or potential energy '. A head of water represents a 
certain amount of moving power by its very position. This 
energy may not be evoked, and may exist for ever only as 
potential. Yet it is as really existing as when it is employed 
to turn a wheel. 

(2) The different forms of energy may, under certain ar- 
rangements, be transmuted one into the other. Mechanical 
force may pass into heat, and heat into mechanical force : an 
energy of motion may be exchanged for an energy of position 
and conversly. The rate of exchange is invariable. 

(3) In the interchange of energies nothing is lust. In every 
case where energy disappears by resistance, and is seemingly 
lost, a definite equivalent of heat is generated. 

If we suppose a portion of the universe isolated so that it 
neither gives nor receives energy from without, then the 
principle of the Conservation of Energy asserts that the sum 
of the kinetic and potential energies within this material system 
is constant and unalterable. The actions and reactions of its 
parts can only vary the relative projtortions of kinetic and 
potential energies, but not their amount. 

Of these three circumstances the first matter in motion or in 
position, is the definition or generalisation of force or energy; 

F 



L >; (1 > CAUSATION AS CONSERVATION OF FORCE. 

the second, transmutation of one form of power into another; 
and the third, conservation of the sum of the energies of 
motion and position of any self-contained system, under all 
ohnncres, are the properties or predicates, constituting the Law 
of Correlation or the Conservation of Energy. 

10. In explaining the principle of Conservation as 
applied to the different forms of actual energy, we may 
rank them in two divisions, Molar and Molecular, — 
motion in mass and motion in molecule. 

The Molar Forces are the same as those termed 
Mechanical. 

The molar or mechanical forces are the motions of sensible 
masses, as a hammer, a waterfall, a locomotive, a planet. The 
science of Mechanics, or Molar Physics, is occupied with the 
computation of these forces, in their transfer aud rs-distriba- 
tion under all varieties of circumstances. 

The Persistence or Conservation of Force was first distinctly 
conceived with reference to these palpable motions. Newton's 
First Law of Motion expresses the fact that a mass once iu 
motion will, if unobstructed, always continue in motion at the 
same rate ; which is the same as saying that force never 
decays. In free space, beyond the reach of molestation from 
without, a moving body would preserve its motion for ever. 
This is the simplest aspect of Conservation. 

A moving body encountering a second body, whether at rest 
or already in motion — (1) if we suppose both bodies to be per- 
fectly elastic — imparts its own motion, in whole or in part, to 
the body struck. This is a new situation. There is a loss of 
power on one side, and a gain . on the other ; a redistribution 
of the movements of the two masses. Now, in this state of 
things, the Law of Conservation declares that in the inter- 
change nothing is wasted ; whatever the striking body loses, 
the struck body gains. 

If the two masses are equal, there will be simply an in- 
terchange of velocities, and of momenta ; and if they are not 
equal, still the impact will not alter either the total momentum, 
or the moving energy of the whole. 

(2) When the bodies are inelastic, then the visible energy 
will disappear in whole or in part. If a contemporary of 
Newton had been asked what becomes of the force of cannon 
shot arrested by a dead wall, he would probably have answered 
that an iunnitesiraally small movement was imparted to the 



CONSERVATION OF MECHANICAL Fo|; 

mass of rock and its contiguous material. This would l KW o 
been regarded as a consistent following out of t\w, theory of 
conservation in communicated momentum. The lost energy 
of the quick- moving ball would exist as energy in a buira 
mass very slowly moving. 

Had the farther question been asked — what becomes of the 

force of two opposing movements destroying one another 

the above answer would not have served the purpose. No 
motion is created in any form ; there is nothing to appearance 
but sheer waste on both sides. 

The new difficulty would in all likelihood have been met by 
a very plausible assumptiom. It might have been said that 
the conservation of force was to be interpreted as force operat- 
ing in the same direction ; all forces in the opposite direction 
being held as negative quantities, like debt to credit. It would 
be a sufficient account of any force that it had neutralized an 
equal and opposing motive force; as when a payment of a 
hundred pounds to any one's credit extinguishes a hundred 
pounds of debt. 

Yet this explanation is fallacious as a principle, and in 
opposition to the facts of the case. Two bodies moving in 
opposing directions are not to be compared to positive and 
negative; each' has a positive value, for any purpose whatso- 
ever. Two streams running in opposite directions, are as 
good for mill-power as two streams moving in the same 
direction. Easy mechanical contrivances can, without loss, 
divert a moving power into any direction. The two opposing 
forces that by collision extinguish one another, could by a 
suitable arrangement, unite their power in the same course. 
The destruction, therefore, that ensues in a hostile collision, 
is (on the present assumption) pure destruction, unredeemed 
waste, annihilation. It is at variance with the Law of Con- 
servation, which would have to be restricted and qualified to 
moving bodies always following the same course. 

The principle of Conservation has been rescued from this 
perplexity by the discoveries of recent times. If two in- 
elastic bodies encounter and arrest one another's movements, 
the mechanical or molar energy is indeed sunk ; but re-appears 
in an equivalent energy communicated to the molecules, and 
manifested as Heat The molecular motion excited in the 
encountering masses is exactly equal to the molar energy 
consumed. This is an entirely new view of Force ; and 
saves the principle of Conservation, by giving it an 
enlarged scope. It teaches us to take account of all the 



254 CAUSATION AS CONSERVATION OF FOKCE. 

protean transformations of energy, and prevents us from 
rashly declaring that force is destroyed when it has ceased to 
appear in the original shape. Mechanical force in some cir- 
cumstances, well understood, yields mechanical force ; in other 
circumstances, for example, hostile collision, it yields a mole- 
cular force, namely, Heat. 

Goino- back upon the first query propounded to a contem- 
porary °of Newton, — the account to be given of a ball's 
impinging on a dead rock, — we should now answer the ques- 
tion not by mechanical transference — a slow motion imparted 
to the rock — but by molecular transformation. The bail and 
the place where it struck would both be found to rise in tem- 
perature, and the more as the moving force of the ball was 
greater. All the energy would be accounted for in this way. 
Iu every case of collision, and even of impact without opposi- 
tion, something is lost by conversion into heat. The loss of 
power by friction is a generation of heat. 

11. The Molecular Forces may be provisionally enu- 
merated as follows : — (1) Heat, (2) Chemical Force, (3) 
Electricity, (4) Nerve Force, (5) Light. 

This enumeration is to be held as provisional ; it may not 
include all the species ; and it may represent, as distinct kinds, 
what are only slight modifications of one kind. 

(1 ) Heat — Probably the best example for showing the mole- 
cular forces, in their contrast to the molar, or mechanical, is 
Heat. Our experience of this influence is abundant and 
various. Yet, only of late years have we been led to call it a 
form of moving matter, a species of molecular motion or 
vibration, which bursts forth on the shock that extinguishes a 
mechanical impetus. 

Such shocks of mechanical collision are the usual mode 
of transmuting mechanical energy into heat. Friction is 
only a more gradual and protracted collision. A familiar 
illustration is seen in hammering a piece of cold iron till it 
becomes red hot. The high temperature of the sun is hypo- 
thetically accounted for by collisions of enormous swift-moving 
masses, brought together by gravity. 

Such is the situation for converting mechanical motion 
into Heat. The transmutation of heat into Mechanical 
force, is effected through the expansion of bulk caused by 
raising the temperature of bodies. In solids, and in liquids, 
this expansion is small in range, but great in force ; and is 
adapted only to special cases, as the splitting of rocks, where 



MOLKCULAK FORCES. 

there is need for a great power moving only a very little 
Through the medium of gases, the expansion can be converted 

into mechanical energy, in any form we please, as in the 
diversified performances of steam power. 

In generating mechanical power by heat, as in the si earn 
engine, the source of heat must be of a higher temperature 
than the medium; the fire must be hotter than the water and 
the steam. The power is given forth by the descent^of the 
heating body to a lower temperature. Between bodies equally 
hot, there is no development of mechanical power, no forcible 
expansion of any one body. 

There is a peculiar incontinence attaching to the Heat 
force. We usually find that some body possesses it in such 
superior degree as leads to radiation upon other bodies, with 
loss to the radiating body. This is the moment for obtaining 
a mechanical or other equivalent. It is also the moment of 
dissipation of energy without equivalent, if the opportunity is 
not turned to account. The solar heat falling on the planets 
gives an equivalent in raising their temperature, and in pro- 
ducing other forces ; what is not intercepted is at once dissi- 
pated into empty space, without farther result than to elevate 
by a slight addition the general temperature of space ; a real 
but unavailable equivalent of the heat lost to the sun. 

It is as regards Heat that the rate of exchange with 
mechanical force has been settled with the highest numerical 
precision. The assumed unit of mechanical energy is the 
foot-pound of England (and the metre-kilogramme of the 
Continent), meaning the force expended in raising one pound 
weight one foot. The unit of heat is defined as the 
amount that must pass to one pound of water in order to 
raise its temperature (or sensible heat motion) by one 
degree of the thermometer. The rate of exchange or 
equivalence is 772 foot-pounds to one pound of water 
raised 1° Fahrenheit ; or 1390 foot-pounds to 1° Centigrade. 
In the Continental scale of weights and measures, the 
expression is 425 metre-kilogrammes to one kilogramme of 
water raised 1° Centigrade. By a perfect machinery of 
conversion of heat into mechanical power, the heat requisite 
to boil a gallon (ten pounds) of freezing water would lift 
1380600 pounds one foot. 

(2) Chemical Force. — Energy, in a form adapted to separate 
chemical compounds, and as it appears when bodies combine 
chemically, is chemical force. When water is decomposed into its 
elements — oxygen and hydrogen — a certain amount of force is 



CAUSATION AS CONSERVATION OF FOKCE. 

absorbed or used up in order to bring about the decomposi- 
tion ; and the same force reappears when the elements are 
• mbined. 

This ahemical force is a very slight modification of Heat 
In the case of combination, the force evolved appears as heat 
in its common form. Indeed, our artificial heat of combus- 
tion, is the chemical force liberated in the chemical combina- 
tion of oxygen and carbon (supposing coal or charcoal to be 
tLe fuel). By peculiar arrangements, this force of combination 
may be prevented from appearing as sensible heat, and may 
take other forms ; it may decompose other compounds (as in 
the double decomposition of salts) ; or it may pass into elec- 
tricity or into magnetism. 

Again, Heat may operate as a decomposing agent. Many 
compounds are decomposed at once by the application of 
heat, as the oxides of the noble metals. A familiar example is 
the decomposition of chalk or carbonate of lime, in a lime 
kiln ; the heat drives off the carbonic acid, and what remains 
is burnt lime. Other compounds are decomposed by heat, 
when there is an arrangement for combining one of the de- 
composed elements with a third snbstance ; as when water is 
decomposed in a red-hot iron tube, the oxygen combining with 
the iron. 

That heat, the result of combination, should be the means 
of decomposition, is the proper, the natural consequence of 
the Law of Conservation. Whatever is given out when ele- 
ments combine, must be restored when they separate again. 
This is the exact relationship of heat to chemical action, which 
is disguised and apparently reversed by the familiar employ- 
ment of heat to make bodies combine, as in lighting a 
fire. The application of heat in such a case, however, is a 
mere incident ; it seems to operate by disturbing the quies- 
cence of the elements. It no more renders heat a combining 
power, than the pailful of water thrown into a pump before 
pumping is the cause of the subsequent flow. 

The rate of commutation of Heat and Chemical Force, has 
to be given in the detail, inasmuch as different compounds 
give forth different quantities. I quote as examples" a few 
oxygen compounds. One pound of hydrogen burnt (that is, 
combined wilh oxygen) would elevate,' by 1° C, about thirty- 
four thousand pounds of water. This is the most heating of 
all oxygen combinations ; we have long been familiar with°the 
intense heat of the oxy-hydrogen blow-pipe. Of simple 
bodies burnt, or combined with oxygen, the next in rank, is 



HEAT.— ELECTRICITY. 

Carhon, the chief ingredient of ordinary combust ion, nnd also 
of animal combustion. The figure for carbon is less than one 
fourth the figure for hydrogen ; a pound of carbon bdrnt 
elevates, by 1° C, abouc eight thousand pounds of waiter, 
Phosphorus ranks next among the simple bodies examined 
(674:7 pounds) ; then sulphur (2307) ; the metals, zinc, iron, 
and tin, are nearly equal (zinc, J 301, iron, 157o\ tin, 1223); 

(3) Electricity. — This variety of moleeular foree is distin- 
guished by two main peculiarities. The first is polarity, or the 
development of opposite forces at opposite points ; the magnet 
is the most familiar example of the power, operating in masses 
of matter. The second is named conduction, and means the 
rapid transmission of the force from one part of a body to 
another, along a wire, for example ; a process of conveyance 
quite different from any of the modes of the transmission of 
heat. An electrical charge passes almost instantaneously, and 
with little diminution of force, through miles of copper wire. 

The name * Electricity * now includes various phenomena 
marked by characters widely different. Three types or species 
may be indicated — Magnetism, Friction or Franklinic Elec- 
tricity, and Voltaic Electricity : all these have a molar 
as well as a purely molecular side ; the last is in close 
relation to chemical force. Magnetism, as a member of the 
group of Correlated Forces, under the Law of Conservation, 
is best studied in the form called Electro-magnetism, or mag- 
netism generated from electricity ; for, while the magnetism, 
which is a mechanical attraction, can be estimated by its 
mechanical effects, the electricity can be estimated chemically 
by the amount of acid and zinc combined in the cells of the 
battery. Friction Electricity, in the common electrical machine, 
is generated by mechanical force (sometimes by heat, as in 
crystals); its discharge, being marked by vehemence, concentra- 
tion, or intensity, is not measurable with accuracy ; the effects 
are seen in the rupture of atomic cohesions, in strong outbursts 
of heat and light, and other indications of concentrated force. 
Voltaic Electricity is the species most closely allied with 
Chemical Force ; which force is its source, its measure, and 
one of its results. Through chemical force, as measured by 
the amount of material chemically combined in the voltaic 
cells, we can state the rate of exchange or commutation of 
Voltaic Electricity with Mechanical force, and with iieat. 

These three modes of Force — Heat, Chemical force, Elec- 
tricity — are the well-defined species of molecular activity; 



258 CAUSATION AS CONSERVATION OF FORCE. 

thov can all be measured and put into strict equivalence with 
Mechanical Energy. There still remain, however, Light, 
nixl anv modes of activity in living bodies, distinct from, and 
superadded to the forces of the inorganic world ; the Nerve 
: ce is one well-marked example. From the close analogies 
between this last-named force and Electricity, we may take it 
next in order. 

(4) Nerve Force. — The Nerve Force is the special activity of 
the nerves and brain. Like Electricity, it is a current force. It 
differs from Electricity in moving at a comparatively slow rate ; 
and also in depending for its maintenance upon chemical com- 
binations in the material of the nerves ; hence, while electricity 
docreases as it goes, the nerve force increases. Although this 
force cannot be subjected to accurate measurement, we con- 
clude from analogy that there is an exact equivalence between 
it and the chemical transformations that are its source ; part 
of the food of the body is expended in supplying it. It con- 
tributes to muscular power, in which case it has a mechanical 
equivalent; and to molecular changes, chemical or other, also 
on a definite rate. As the physical concomitant of mental 
states, we must still regard it as definitely related in quantity 
to these ; a double amount of feeling, other things being the 
same, involves a double amount of nervous transformation. 

(5 ) Light. — The divorcing of Light from Heat, in the enu- 
meration of the molecular forces, needs to be explicitly justified. 
The divorce is at best provisional and temporary ; the reasons 
are such as the following. Although Ligdit is a distinct product 
ot the other forces, more especially Heat, and is instrumental 
in causing at least one of them, Chemical force, yet hitherto 
nothing has been done towards establishing the rate of com- 
mutation or exchange between it and the others. When a 
body is heated till it becomes luminous, there ought to be a 
definite loss of heat, equivalent, on a certain scale, to the 
light produced ; at present, however, we have made no ap- 
proach to such an estimate. Moreover, although light is 
the instigator of chemical change, we cannot say that it'oper- 
ates by supplying chemical power, as heat or as electricity 
does ; the effect may be similar to the action of heat in lighting 
a fire, a mere disturbance sufficing to begin the chemical 
union of elements ready to combine. Chlorine and hydrogen, 
mixed together, will not combine chemically in the dark; the 
combination begins under the light. It is to be remarked, 
however, that dccompositio?i is the direct test of chemical force. 
Kow, light will not cause decomposition unless in the presence 



POTENTIAL BRXBOT. 

of a body, like hydrogen or chlorine, haying a pnv. 
tendency to combine; or, when, as in vegetation, light is 
accompanied by heat. We are, therefore, led to regard light 

chiefly as the prompter to a change otherwise maintained. 
in this view there is a numerical proportion 1> oount 

of light and the extent of the chemical action ; as shown in 
the researches of Bansen and Hoscoe (Phil. Trans., [-■',. 

When mechanical force operates against gravity, as when 

a projectile is thrown upwards, the force is at last spent ; the 
equivalent gained is a j^ositlon of adccnitcuje, with respect to 
gravity; for, by the continued operation of the gravitating 
energy, the whole of the impetus lost will be restored in the 
downward direction (the resistance of the air being left out 
of the account). We are familiar with this employment of 
gravity in clocks propelled by weights regularly wound up to 
a height. To this peculiar situation, Prof. Rankine haa 
applied the name l potential energy/ to distinguish it from 
the energy of a mass in actual motion. The placing asunder 
of the celestial bodies, all which gravitate towards each other, 
was the primeval situation of advantage, whence may have 
arisen (by collisions) the heat of our suns and planets, and by 
consequence all the other modes of force — mechanical, chemi- 
cal, and electrical. 

It is by this operation that the force of gravity is introduced 
into the circle of forces, and is counted as a cause or productive 
agent. Viewed in itself, it creates no force; what is paired 
in visible force is lost in position ; to restore the position 
would require the power to be given back. It can, however, 
divert power; it can also store up and re-distribute it, as a 
banker does money. 

A similar position of advantage may be found in the mole- 
cular forces. Thus, the existence of two elementary bodies, 
able to combine, is a potential chemical energy, which, on the 
occurrence of the opportunity and the stimulus, is converted 
into actual molecular energy. Such is the potential force of 
our coal, and of all the uncombined and combinable e'ements 
of the globe,— as native sulphur, the native metals, an 
lower compounds susceptible of entering into higher com- 
pounds. 

The molecular attractions of bodies (as cohesion) may oper^ 
ate exactly in the manner of gravity. A spring is an obvious 
example. The elasticity of compressed air may be turned to 
the same account. 



2C0 CAUSATION AS CONSERVATION OF FORCE. 

12 Causation, viewed as Conservation, is thus the trans- 
ferring or re-embodying of a definite amount of Force. 

When a ship is propelled by wind or by steam, the motion 
is said to be caused by those agents ; which expend themselves 
in producing the effect. The expansiveness of steam is due to 
heat operating through the medium of water. The heat arises 
from the combustion or chemical union of coal and oxygen. 
The coal was the carbon of plants of former ages, whose 
grbWth demanded an expenditure of solar heat. 

So, again, in the human body, mechanical force is obtained 
by mucsular exertion ; that exertion is owing to the oxidation 
of* the materials found in the blood ; these materials are either 
vegetable products, or the bodies of other animals fed on 
vegetables ; and, thus we com© round again to the agency of 
the solar ray in vegetation. 

Transferred energy is thus the final and sufficing explanation 
of all change, and the only explanation in the highest sense of 
the word. Any fact of causation not carried up into this 
supreme law, may be correctly stated, but it is not accounted 
for. 

Whatever appearances militate against the principle of Con- 
servation are to be held as fallacious. The ' perpetual motion 
has long been rejected as incompatible w r ith the mere mechani- 
cal phase of theprinciple. There still remain to be removed 
various errors against the more comprehensive view. For 
example, the incautious remark is frequently made that Light 
is the operative cause of vegetative growth, meaning light 
alone ; but the large amount of chemical power required to 
decompose water into its elements (the bodies of all others 
most costly in their demands) could be furnished only by the 
heating rays of the sun ; however much light may co-operate 
in giving stimulus or direction. 

13. The Law of Conservation exhausts Causation, viewed 
as the transfer of Force or Moving Power, but leaves many 
complicated, and, as yet, unsolved questions of Colloca- 
tion. 

If we view causation as the transfer or re-distribution of a 
certain definite amount of moving power, nothing can be 
simpler than the statement of the principle ; and, in many 
instances, we find it easy to make the exact calculation. But 
the circumstances attending the transfer, the situation or 
collocation of the materials engaged, may have all degrees of 
complexity. 

i 



COLLOCATIONS. 

The simplest situation is the transfer of mechanical power 
by impact, as when a golf ball is impelled by the momentum of 
the club. At least, we usually suppose this to he # a simple 
case; we take no account of the internal agitations of the 
particles of the body struck, being content to assume thai, the 
momentum is transferred with inconsiderable loss. llnv, 
then, the collocation is the easiest possible; it is the sensible 
contact of one moving body with another, either at rest or 
already in motion. Even when one moving body strikes 
another moving in a different direction, the difficulty of tho 
collocation is not much increased ; the mechanical theorems of 
oblique forces will predict the new distribution, and assign tho 
directions after the impact. 

When we pass from the interchange of mechanical forces, to 
the mutual interchange of mechanical and molecular, we en- 
counter situations or collocations of various degrees of com- 
plexity. Least difficult is the relation of mechanical energy 
to heat. When a moving body encounters a dead resistance, 
the whole of the energy is resolved into molecular motion of 
the encountering masses ; if the body struck gives way in 
part, and takes on motion, the actual energy generated is so 
much deducted from the energy transformed into heat. 

The transfer of heat into mechanical force, as in the steam 
engine, is accomplished by the expansiveness of the heated 
matter. Starting from the fact of forcible expansion, the con- 
version is merely an instance of mechanical impact. The 
difficulties are postponed to the next stage. 

The interchange of Heat and Chemical Force, the production 
of each from the other, at will, is effected by an arrangement 
that can be expressed with considerable definiteness in the 
gross, although leaving the ultimate links of transition in deep 
obscurity. The active combination of two combinable bodies, 
as carbon and oxygen, evolves heat ; but the minute circum- 
stances of the evolution can be only hypothetical!}) surmised. 
The intestine heat motions of carbon and of oxygen, in their 
separation, when transferred to the joint curbonic acid mole- 
cules, are in excess, and the surplus gives elevation of tem- 
perature, or sensible heat, to the mass. 

The re-conversion of Heat into Chemical Force (potential), 
as in chemical decompositions, is somewhat more complicated, 
but an account can be given of the situation in gross. In the 
cases where decomposition is effected by heat alone, we have 
the simple restoring of the surplus heat of the combination. 
In the other cases, where a new combination must be formed, 



I 



CAUSATION A3 CONSERVATION OF FORCE. 



we have an additional circumstance, still perfectly definable, 
and, in a rough manner, hypothetically conceivable. 

The difficulties of Collocation grow thick upon us when we 
grapple with the Electrical group of forces. The polarized 
state of matter, whether in mass, as the magnet and the 
Leyden jar, or in molecule, as in the decomposing cells of the 
voltaic battery, is a new and unique phenomenon ; and its 
generation by mechanical force or by heat may be stated in 
the extreme terms, but without intermediate explanation, 
even by a plausible hypothesis. After many laborious tenta- 
tives, Faraday discovered the arrangement for directly convert- 
ing mechanical power into voltaic electricity (commonly called 
the magneto-electric machine), but the links of the transition 
or intermediate molecular changes are as yet unassignable. 

Yet worse perplexities surround the collocations for trans- 
ferring force in Living Bodies. Even the simplest case — the 
production of Animal Heat from chemical combination or 
combustion — is anomalous when compared with the same 
phenomenon out of the body. The general fact is oxidation, 
but the circumstances and arrangements are peculiar and 
unknown. Again, the production of Muscular Force from the 
process of oxidation is in accordance with the Law of Conserva- 
tion, while the transition links are hitherto inscrutable. Like- 
wise, the Nerve Force has the same common origin in chemical 
transformations (or closely allied molecular transformations) 
as the other forces, and follows a regular rule of exchange, 
while the mode of derivation is involved in obscurity. 

14. Seeing that, in Causation, there must be provided, 
not merely a sufficient force, energy, or moving power, but 
also the suitable arrangement for making the transfer as 
required ; this completing arrangement, or collocation, is a 
part of the Cause, and (by ellipsis) is frequently spoken of 
and investigated as the Cause. 

A running stream is the proper source of the energy that 
turns a mill. In order to the effect, however, the due colloca- 
tion or connexion must be made for bringing the water to 
bear upon the machinery. Hence, the stream being taken for 
granted, the cause of the grinding of the corn is the providing 
of machinery, and the regulation of the sluices ; which circum- 
stances are of the character, not of force, but of collocation. 

So, in a Voltaic Battery, intended to decompose water, or 
to excite an electro-magnet, the prime mover is chemical 
force arising in the cells of the battery; the completing 



UNKNOWN COLLOCATIONS. 

arrangements include the whole apparatus of the battery, ami 
the final act of closing the circuit. 

The combination of the food materials with the oxyge 
the air, may be reckoned the source of all annual power; 
but so numerous are the conditions to be secured in 
way of arrangement or due collocation, that we have often 
to think far more of these than of the propelling agency de- 
rived from the primal source of all moving power. \Y r e not 
unfrequently assign as the cause of a man's bodily strength, a 
good digestion, healthy lungs, or a good constitution generally, 
and say nothing of the real derivation of the strength; the 
reason being that, without the complex group of arrangements 
implied in these facts, the power would not be transferred from 
the common fund and embodied in the man's muscular and 
uervous energies. 

When a man properly supplied with food, goes through a 
day's work, we recognize a transfer of moving power, under 
the Law of Conservation. When any* one prostrate with 
weakness is restored to strength by a few drops of laudanum, 
there is no proportion between the cause and the effect, con- 
sidered as moving power giving birth to equal, although 
different moving power. The salutary interference must be 
regarded, not as a communication of moving energy corres- 
ponding to the access of energy that follows, but as the restor- 
ing of some arrangement cr collocation, necessary to the 
conversion of the body's nourishment into the various forces 
of animal life. 

As our knowledge of the Law- of Conservation is such as to 
account for the remote source of all power whatsoever, the 
enquiry usually presented for scientific investigation is by 
what arrangements a given effect has been secured, or through 
what media the bank of Nature's Force has been drawn upon 
in the particular instance. Not many years ago the pheno- 
menon of volcanoes was regarded as wholly mysterious ; since 
the establishment of the Law of Conservation, all that part of 
the mystery connected with the source of the upheaving power 
has been removed. It is the internal heat of the earth con- 
verted at certain points into mechanical energ}\ What re- 
mains for scientific investigation is a pure question of collocation; 
we are still ignorant of the arrangements for effecting the 
transference of power in that particular manner. 

In the same way, all the great cosmical changes, marking 
the evolution of the solar system, and the geological history of 
the earth, are referable to the primal sources of energy ; the 



CAUSATION AS CONSERVATION OF FOKCE. 

moving power at work is no longer a secret. Yet the circum- 
Btances/ arrangements, or collocations, whereby the power 
operated to produce our existing mountain chains, the rise and 
fall of continents, the fluctuations of climate, and all the other 
phenomena revealed by a geological examination of the earth, 
arc as vet in uncertainty. 

1,5. The importance of Collocation appears in another 
aspect, as representing the modes of Potential Energy. 

Potential Energy is energy of situation, arrangement, or 
collocation. The Potential Energy, stored up when moving 
bodies work against gravity, till their force is exhausted, is 
described as a position of advantage, a collocation of power, 
with reference to a gravitating mass. Here we have the re- 
markable case of force embodied in absolute stillness or quies- 
cence. A mountain tarn is absolutely quiescent while its 
enclosure is perfect ; the immense impetus to be displayed in 
its descent to the plains is not at present represented even by 
molecular motion. 

A similar energy of collocation is created when bodies are 
distended in opposition to their cohesive attractions, as in 
springs. 

Lastly, there is the energy of separation of Chemical ele- 
ments, as in coal, sulphur, metals, and other combinable sub- 
stances, simple or compound. Gunpowder is a concentration 
of potential chemical energies, or of combinable elements in a 
situation of readiness to combine. 

It is in the case of these potential energies that we seem to 
create moving power, to bring forth force, without a prior 
equivalent force, to make small causes yield great effects. The 
apparent cause, or antecedent, of a great outburst of moving 
power, is something altogether trivial, as if force were 
evoked and absolutely created. Cause and Effect cannot, in 
such instances, be stated as one moving power transmuted into 
an equal moving power, molar or molecular. A child's touch 
might be made to discharge a man-of-war's broadside, or 
inundate a village. One word of a general, the signature of 
a sovereign, may destroy an empire. 
_ Cause, in all these instances, has a peculiar and important 
signification. It is not a moving force equal to the visible 
energy of the effect, it is the exertion, however easy, that 
changes a situation of potential energy to a situation of actual 
energy ; the cutting of the string that suspends a weight, the 
drawing of a sluice, the setting a light to a combustible, the 
supplying of a motive to human volition. 



ENQUIRY INTO COLLOCATIONS. 

The course of experimental investigation must adapt its 
this position of our knowledge as regards Causation. We 
know the ultimate, and, in most instances, tlio proximate 
sources of moving power or energy ; we know a c 
number, more or less, of the conditions or collocations of t)u- 
transfer; what we still desiderate is the thorough and full v 
generalized knowledge of the remaining collocations. 

In the subtle actions of Light, we are at this moment in 
doubt whether the luminous raj operates as a dynamical 
and force-giving agent, like Heat and Electric Force, or only 
as a collocating agent, either to complete the medium for 
transmitting a true force, or to convert a potential into an 
actual force. As causing chemical combinations, we can 
ascribe to it nothing more than the liberation of the potential 
chemical energy. So, in acting on the eye to rouse our 
optical sensibility, it may be no more thau a disturber of 
latent forces. 

The settling of this preliminary point is necessary to our 
progress in the investigations of luminous agency. In merely 
completing, or else disarranging collocations, Light must 
exert a dynamical force, but it may be of the very slightest 
amount, and out of all proportion to the results that ensue. 
There is no proof that, in any situation, the energies aroused 
by light are maintained at the cost of the light. 

The character of a disturbing agent must attach to many, if 
not most, of our sensations. The tickling of the nose by the 
proboscis of a fly cannot be the source of the muscular move- 
ments that arise from the feeling. The irritation of a musical 
discord, the revulsion at an odour, the energetic discharge of 
a bitter morsel from the mouth — are efficacious as disturbing 
some collocation, and bringing potential force into actuality. 

In the complicated animal framework, there may be violent 
displays of energy consequent on the withholding of the 
regular supplies of energy. Extreme hunger may lead to 
nausea and retching. In the delirium of fever, when no 
nourishment can be received, there is great muscular exexHion. 
We are at no loss, on the foregoing principles, to solve the 
apparent contradiction. 

16. As Cause may not always mean the Moving Power 
transferred, according to the Law of Conservation, so, the 
Eif'ect may not always mean visible energy gained, but a 
new arrangement or Collocation of materials. 

Moving Power is often expended, not with a view to repro- 



966 CAUSATION A3 CONSERVATION OF FORCE. 

dncin- some equivalent power, but merely to re-distribute 
materials, as in transporting stones from a quarry to erect a 
building There is a definite expenditure of power, corres- 
ponding to the collective amount cf the stones, the distance, 
and the friction of the roads ; but the wbole effect consists in 
a change of position of the materials, witbout any available 

encr <r y • 

Such is the nature of many Geological changes. When the 
forces of the earth and the sun raise mountains, they impart a 
position of advantage, or of potential energy ; whereas the 
transport of erratic boulders, the deposition of strata at a dis- 
tance from the source of the material, are effects of change 
without any embodiment of moving power. 

17. The evidence for Causation and for Conservation is 
the same. 

This follows from the identity of the principles. Now, as 
previous to the announcement of the principle of Conserva- 
tion, a great body of evidence had been accumulated in favour 
of Causation in the old form, all the experimental proofs in 
favour of Conservation are a pure addition to the evidence of 
Causation. In point of fact, however, these experimental 
proofs are themselves considered .adequate to establish the 
principle of Conservation. 

Those speculators that rely on an intuitive basis of proof 
for this grand generalization treat the two forms as identical. 
Thus, Sir W. Hamilton is singular among metaphysicians, in 
giving to the Law of Causation a form almost exactly co-inci- 
dent with the principle of Conservation, which he may be said 
to have anticipated. 

Mr. Herbert Spencer holds that * the total quantity of matter 
in the Universe, cannot really be conceived as diminished, anf 
more than it can be conceived as increased. Our inability to 
conceive Matter becoming non-existent, is immediately con- 
sequent on the very nature of thought. Thought consists in 
the establishment of relations. There can be no relation estab- 
lished, and therefore no thought framed, when one of the 
related terms is absent from consciousness. The annihilation 
of Matter is unthinkable for the same reason that the creation 
of matter is unthinkable; and its indestructibility thus be- 
comes an a priori cognition of the highest order — not one that 
results from a long-continued registry of experience gradually 
organized into an irreversible mode of thought : but one that 
is given in the form of all experiences whatever ' (First Prin- 



EVIDENCE FOR CAUSATION. o,;; 

01PLES, 2nd edit. p. 175). So much as regards Matter. Now 
as Matter is known to us merely as exerting force, the reason* 
ing really applies to Force as tho underlying experience, the 
real signification of Matter. Hence, * by the indestructibility 
of matter, we really mean the indestructibility of the l'<>: 
with which Matter affects us.' 

Without re-entering into the controversy as to the best of 
truth furnished by the inconceivability of tho opposite, wo 
may remark that in the absence of experimental confirmations 
and interpretations, such an a priori conception would be very 
hazardous to rely on. It would not tell us, for example, th;it 
all the force of nature seems tending to a mode o/ dissipation 
which is, to all intents and purposes, annihilation, namely, tho 
radiation of heat into space. Moreover, the case has already 
been adduced of two opposing forces meeting to neutralize one 
another ; a fact formerly accepted as in full consistency with 
the indestructibility of mechanical force ; the universal belief 
of scientific men, as well as of others, was that nothing survived 
such a collision. Such a priori renderings are of the nature of 
prophecies made after the event. 

When the Inductive Methods have been fully explained, the 
proof of the Law of Causation will be reverted to wish a view 
of indicating its logical character. We here assume it as 
sufficiently established, and we shall have to proceed upon it 
deductively in several of the methods of Inductive Proof and 
Elimination. Without it, there could be no short cut to the 
establishment of a law of nature ; every separate induction 
would have to be proved by a detailed examination of instances 
through all nature. The most potent of the Inductive Methods, 
the Method of Difference, is a deductive carrying ou-t of the 
law of Causation or of Conservation. 

18. The Cause, or aggregate conditions, of an Effect 
must be sought among the antecedent circumstances con- 
joined with it. 

To appearance, Cause and Effect are a sequence or succes- 
sion ; the cause being first, or the antecedent ; the effect, 
second, or the consequent. It is, therefore, among the circum- 
stances preceding the effect, and in sufficient connexion of 
time and place, that we look out for the cause. 

The main difficulty of the determination is due to the fact 
that, in most cases, circumstances not entering into the cause 
are also found among the antecedents, in as close connexion of 
time and place as the causal conditions. It is to extricate the 



THE COMPOSITION OF CAUSES. 

ml conditions that we must enter on a course of observation, 
experiment) and comparison of instances. 

19. An invariable antecedent is not necessarily the cause 
or any part of the cause of an effect. 

The familiar example is the sequence of day and night ; 
which, although invariable, is not a sequence of cause and 
effect. So in the evolution of a living being, there are numer- 
ous links of invariable succession ; and yet we are not entitled, 
on that circumstance alone, to pronounce the earlier the cause 
of the later. 

The case of day and night, being an understood phenomenon, 
illustrates the difference between causation, and mere invaria- 
bility of order. We know that the cause of day, is the light of 
the sun falling upon the earth ; that the cause of night is the 
absence of the sun. We farther know that the earth's rotation 
is the circumstance occasioning the periodical absence of the 
light. The cause of this entire phenomenon is made up of — the 
luminosity of the sun, our being placed within reach of that 
luminosity, and the earth's rotation about its axis. The 
alternation of light and dark is itself but a consequence — a co- 
effect of the assemblage of facts constituting the phenomenon. 

Some of the invariabilities of vegetable and animal growth 
may be proved, and others presumed, to be only common effects 
of the real cause. 

Such invariabilities are part of the difficulty of causal 
elimination. 

The cause must be an invariable antecedent, but it must 
farther be what Mr. Mill expresses as the ' unconditional in- 
variable-antecedent/ the sole sufficing circumstance whose 
presence makes the effect, and whose absence arrests it. Day- 
light is preceded by darkness ; but a state of darkness is not 
everywhere followed, after a certain duration, with day-light. 
We cannot, in the case of day and night, separate darkness from 
its order of alternation with light ; but, in referring to other 
cases, and other situations, we do not find that a present dark- 
ness always alternates with illumination. 

THE COMPOSITION OF CAUSES. 

20. When several motive powers are conjoined, the com- 
posite effect is the sum or difference of the separate effects, 
according as they conspire with, or are opposed to each 
other. 

t 



COMPUTATION OF COMBINED I 200 

Causes, understood as prime movers, may be combined) and 
the result computed by a numerical operation. Two men pul- 
ling at the same rope, two locomotives, two weights, when 
acting in the same direction, have a total effect equal to the 
sum of the separate effects. When they thwart one another, 
the result is the difference. For oblique action, the computa- 
tion is made by the parallelogram of forces. 

In the molecular agencies the same rule applies. Two equal 
fires give twice the heat of one ; two bushels of coals make 
twice the combustion of one, that is, twice the heat ; in the 
steam engine, to double the fuel is to double the motive power. 
Three identical wax candles produce a triple illumination. 
Two equal magnets put together will sustain a double weight. 
It' a voltaic battery of ten cells decompose a pound of water 
in a given time, six similar batteries will decompose six pounds 
in the same time. 

The same principle exteads to the Physiological or vital 
forces.' Increase of heat, light, and assimilating material 
makes a corresponding increase of vegetable growth. Food 
and oxygen actively combined, give forth a proportionate 
amount of animal force. 

Even in Mind, the ratio holds, although interfered with by 
new forces arising out of the complication. The pleasures 
and pains are in accordance with the amount of their several 
agents. A man's enjoyments increase with his gains and 
diminish with his losses, other things being the same. 

The Social forces in like manner combine, and may be com- 
puted by adding the sum of the effects. The additiou of new 
causes of discontent in a people already dissatisfied, makes a 
corresponding advance towards anarchy and revolution. On 
the other hand, some agreeable or soothing agency may neu- 
tralize an ill feeling already at work. 

In all these instances, Cause is to be interpreted as meaning 
Motive Power, or Force ; in no other sense does the rule of 
arithmetical sum and difference apply. Causes that merely make 
good the collocation for bringing a prime mover into action, 
or that release a potential force, do not follow any such rule. 
One man may direct a gun upon a fort as well as three ; two 
sparks are not more effectual than one in exploding a barrel 
of gunpowder. In medicine, there is a certain dose that 
answers the end ; and adding to it does no good. 

21. Composition of Causes is sometimes applied to 
Chemical actions, so as to mean not a union of forces, but 



270 TI1E COMPOSITION OF CAUSES. 

the union of substances or materials. In this way, oxygen 
and hydrogen combine to form water. 

This part of the chemical process comes under collocation, 
and not under force. The mixing of materials, and the union 
of forces, are not the same fact. 

In chemical action, thus understood, we cannot fully predict 
the characters of the compound from the characters of the 
elements. It is the speciality of chemical combination to 
merge nearly all the physical properties of the substances com- 
bined, and to yield a new product, where the combining ele- 
ments are not recognizable. Sulphur combines with copper 
to form a black flaky substance, the sulphuret of copper. 

There are still wanting general laws that would serve us to 
compute the resultant of a chemical combination ; w r e know 
only that weight is not lost, and. that the law of definite pro- 
perties holds. 

The analogy of Chemical Combination has been applied to 
mental and social combinations. Thus, the complex emotions 
of the mind are often so far different from their constituents, 
as scarcely to suggest these to the mental analyst. The moral 
sense, for example, is declared by many to be a simple faculty, 
on the ground of its having no resemblance to any other simple 
elements of the mind. 

Again, in the study of national characters, we may know 
that certain influences concurred in the process of formation, 
and yet find a difficulty in tracing them. 

These, however, are mere analogies. Chemical combination 
is an illustrative metaphor and little besides. The analogy 
fails in one essential circumstance, definite combinations. The 
disguise of the elements or components is the only point of 
similarity : and that would probably be better referred to the 
analogy of groicth, where the constituents entering at one stage 
form a product, still farther combined in succesive operations, 
which cannot all preserve a record of themselves. 



CHAPTER V. 

ELIMINATION OF CAUSE AND EFFECT.— OBSERVA- 
TION AND EXPERIMENT. 

"L The enquiry into causation is usually presented in 
nature as a complication of influences and arrangements, 
some concerned and some not concerned in the cause or 
the effect sought. 

For instance, a man in good health goes to a new place and 
a new occupation. His health gradually fails. There must 
be a cause for the failure; assuming that he could have 
retained his health in his original abode and occupation, the 
cause must lie in the new circumstances that he is placed in. 
These new circumstances are perhaps numerous ; the climate 
may be hotter or moister, not to mention many other variations ; 
the man's new pursuits and recreations may be widely different 
from his old. Now, while some of these differences must have 
some share in the effect, others probably have no share ; and the 
problem lies in disentangling the one class from the other; in 
separating the operative from the inoperative surroundings. 

The case now supposed represents the inductive search in 
its extreme speciality, and as it appears in the commoner 
practical questions. A more general enquiry is exemplified 
in determining the effects of given agents, as heat, moisture, 
electricity, ozone, light, foods or medicines, on the human 
constitution. Every one of those agents has a variety of pro- 
perties, or modes of action ; in the case supposed, some are 
operative and some not; and we must discriminate the one 
class from the other. 

Again, we may propose a still more general enquiry — What 
is the common antecedent to the effect denominated Heat, or 
the peculiar fact or situation always recurring when there is an 
increase in the temperature of material bodies ? In looking 
at the incidents attending the development of heat in any in- 
stance, we find them to be numerous and various ; and we have 
to find some mode of separating the inefficient from the efficient 
elements of the situation. 

We know from the law of Causation, even in the less ex- 
plicit form (Conservation being left out of view), that in the 



872 ELIMINATION OF CAUSE AND EFFECT. 

chancres going on in the world, the present situation is the re« 

suit of the previous situation; and if that previous situation 

re reproduced so would the present. But this is not all ; 

for we may be able to show that if a certain part of the previ- 

3 situation were reproduced, the present would follow; we 

i put aside all otiose or inert accompaniments and reduce 

the antecedent circumstances to those really operative. This 

is the process of Inductive Elimination, required alike in 

special and in general enquiries as to cause and effect. 

Yet farther, we may find the sequence of a past and a pre- 
sent situation to consist in a plurality of distinguishable 
sequences, which we may analyze and isolate by the methods 
to be pointed out. Political causation is almost always a 
complication of many distinguishable threads. 

2. Preparatory to the disentangling or eliminating pro- 
cess, we make, in our own mind, &x± analysis oi the situation. 

As the final end is to discriminate the necessary from the 
unnecessary elements of the situation, we begin by a separate 
enumeration of all the circumstances, taking care to reduce 
each to its simplest components. If a man has lost his health, 
in a certain locality, we first suppose to ourselves what may be 
the distinct agents concerned ; we analyze the climate into all 
its constituent circumstances — temperature, moisture, fluctua- 
tions, purity of air, and so on ; we analyze the peculiarities of 
his mode of nourishment, occupation, habits, state of mind ; 
and the more thorough-going the analysis, the better are we 
prepared for the operation that is to follow. Indeed, an in- 
sufficient analysis will of itself defeat the best laid schemes of 
elimination. Newton's investigation of the planetary motions 
owed its success to his analyzing the course of each planet 
into a centra] tendency towards the sun, and a tangential 
tendency. This separation was the first clue to the mystery. 
In any enquiry into the cause of some effect due to the sun, 
as for example, sun-stroke, the different known constituents of 
the solar beam— heating, lighting, and chemical rays — should 
be separately viewed as the possible cause. 

The ability to perform these mental analyses is partly depen- 
dent on the state of knowledge at the time. Thus, we now 
know, what was not known in the beginning of the last cen- 
tury, the constituents of the atmosphere; we are therefore pre- 
pared for an enquiry, according to the methods of elimination, 
into the precise cause of any atmospheric effect. If it is pro- 
posed for enquiry, why does meat putrefy in the air, we keep 

I 



I 



VARYING THE CIRCUMSTANCES. 

view the distinct constituents — nitrogen, oxygen, m 
carbonic acid, dust, living germs; as among these, or an 
some concurrent action of these the cause must be Pound. 
it is only of late, that the analysis of the solar ray baa indi- 
cated the so-called chemical rays in addition to the: luminous 
and the heat-giving rays. 

It may be farther remarked, that this analytic ability is a 
special mental aptitude personal to the enquirer, and indicat- 
ing the scientific faculty. 

3. In separating the essential from the non-essential 
accompaniments in cause and effect, the course is to vary 
the circumstances, for which end we must resort to Observa- 
tion and Experiment. 

The different antecedents and consequents being separated 
in thought, we have to ascertain which antecedent is connected 
with a given consequent. Having usually a plurality of ante- 
cedents, or a plurality of consequents, or both, we need to 
single out the connected couples of antecedent and consequent. 
This requires us to look for other instances where the group, 
ings are different, and to note what happens when particular 
antecedents or consequents are wanting : an operation described 
by Bacon as ' varying the circumstances.' 

The varied circumstances, or groupings, are so many new 
facts attainable only by Observation, to which we may add 
Experiment. The distinction between these two processes is 
not fundamental, and is seldom important. Observation is 
finding a fact, Experiment is making one. The worth of the 
fact depends on what ifc is in itself, and not on the manner of 
obtaining it. Both methods are used as far as possible. 

The advantages of Experiment are not confined to the 
obvious circumstance of multiplying the facts, important as it 
must often be to multiply them. A second consideration is 
the power that we may have of suiting the facts to the case in 
hand — of producing the sort of variation that we need. Thus, 
in order to ascertain which of the gases of the atmosphere 
supports combustion, or animal life, and what are the elements 
that bring about putrescence and decay, we must, by means of 
experiments, separate artificially one or another of the gn> 
from the rest ; such separation not being provided for us in 
nature. 

Dr. Balfour Stewart remarks, with reference to an investiga- 
tion by Duloug and Petit as to the cooling of a body surrounded 
by a gas, that the research was a very troublesome one, from 



874 ELIMINATION OF CAUSE AND EFFECT. 

tho variations that had to be made in the temperature of the 
body, and in the density, temperature, and chemical nature of 

A third superiority of Experiment over Observation lies in 
the power of producing a phenomenon under known circum- 
stit nee* and surroundings, so as to take account of all extraneous 
influences. Thus, instead of observing electricity in thunder 
discharges, we evolve it in a room where we know all the 
modifying influences. For the examination of magnetism, a 
house is constructed wholly of wood, so that the local disturb- 
ance of pieces of iron may be prevented. Likewise, the best 
opportunity for the study of disease is in hospitals, where the 
sick are wholly under the control of the physician. 

Experiment finds its greatest scope in Physics and in Chemis- 
try. It is admissible in Physiology, iu the Human Mind, and in 
Human Society, with limitations easily divinable by any 
reflecting student. 

In the situation of enquiring into the Cause of a given 
Effect, Experiment is for a moment unavailing. We can try 
the effect of a given cause, but we cannot try the cause of a 
given effect. Assuming heat as an agent, we can make experi- 
ments on its various powers or capabilities ; but given the heat 
of a fermenting mass, as an effect, we cannot, by experiment, 
get out the cause. We must first conjecture a cause ; experi- 
ments may then be instituted to find out the effects of that 
supposed cause; if these tally with the effect in question, 
we have made out our point. 

The problem of Causation may thus be presented in both 
aspects— given a cause to find the effect, given an effect to 
find the cause — but the experimental solution is one ; namely, 
to watch the effect of an assumed cause. The course of the 
phenomenon flows in one way ; cause first, effect second. 
When we seem to be working backward, we are in reality 
working forward. 

REVIEW OF THE COMPLICATIONS OF CAUSE AND EFFECT, 

4. The Inductive Elimination of Causes and Effects may 
be illustrated by a review of the various complications 
actually met with. 

We have already adduced examples of the complications 
that have to be unravelled, in order to assign the neat effects 
of a cause, or the causes of an effect. We are able to present 
a more comprehensive view of the actually occurring entangle- 
ments. 



COMPLICATIONS OF CAUSE AND | 

Those natural aggregates, termed Kinds by pre-. 
are marked by the concurrence, in a single ol 
different properties. Oxygen, carbon, phosphorus, iron, mer- 
cury, platinum— have each a great number of distinc 
or activities ; hence, when the introduction of any one of 
is followed by some change in the things they are brought 
contact with, we are at first uncertain which of all the many 
properties of the substance is the operative circumsi 
Carbon, for example, is found to absorb gases in large amount ; 
which suggests the enquiry, which of the properties of carbon 
is this owing to :— its specific gravity, porosity, blacki. 
amorphous structure, or any other ? Again, mercury has 
certain medicinal effects ; and we desire to know which of its 
many properties is the causative circumstance. Platinum, in 
a finely divided or spongy state, brought into contact witb a 
stream of hydrogen, makes it ignite. What does this depend 
upon ? 

So then, in the elementary bodies of Chemistry, the simplest 
substances known to us, there is a great concourse of anteced- 
ents present whenever any one is brought into play. Out, in 
nature, these are usually found mixed together (I am not 
alluding to Chemical combination, which yields new substances) 
in great varieties of compounds. Thus, the Atmosphere is a 
mixture of two simple bodies — nitrogen and oxygen ; various 
known chemical compounds — water, carbonic acid, and am- 
monia ; and a great many other gaseous effluvia, together 
with solid particles, partly dust and partly ova of plants and 
animals. Moreover, it possesses at each moment a certain 
temperature, a certain electrical condition, and perhaps 
other peculiarities. Thus, when the atmospheric air is pre- 
sented to us as a cause or agency, the possible variety of 
antecedents is very great. Many researches have been occu- 
pied in eliminating the causal conditions in combustion, in 
vegetable and in animal life, in putrefaction, in spontaneous 
generation (so-called), &c. 

Again, the sea is not pure water, but a solution of numerous 
saline bodies. 

Most minerals are mixed substances. A geological stratum 
is highly compound; and when certain vegetables are found 
to grow in a particular soil, elimination must be applied to 
ascertain which are the needful constituents. 

In Vegetable and in Animal Kinds, the complication is 
still greater. The chemical constituents of plants and of ani- 
mals have very complex atoms, whose disintegration may yield 

M 






WEAPONS OF ELIMINATION. 

a variety of different products. Hence, vegetable and animal 
substances used as food, as medicines, as dyes, &c, have many 
possible modes of operating. We must, however, when living 
bodies are agents, farther take into account the organic or living 
structure; the poison of a living plant or animal has powers 
of derangement quite different from the chemical action of its 
chemical constituents. 

The complication in the world of Mind is very great. A 
human being is by nature many-sided, and by education still 
more so. Hence, when one person exercises an influence upon 
another, it is far from obvious, at first sight, by what peculiari- 
ties the effect arises. So again, in the explanation of motives, 
a historian is often baffled to seleot the one that actually 
swayed a given effect. 

The operations of Government are ramified in their conse- 
quences. A single enactment — the imposition of a tax on 
• windows or its removal, free-trade, or its opposite — operates 
variously according to circumstances. 

WEAPONS OF ELIMINATION. 

5. It is in the comprehensive Law of Causation itself, 
once established by Induction, that we have the instru- 
ments for eliminating causes and effects in the detail. 

As already said, there is but one proper Inductive Method 
— Universal Agreement; there is, in the first instance, no 
shorter cut to an Inductive Generalization. We must go 
through the labour of a full examination of instances, until we 
feel assured that our search is complete, that if contrary cases 
existed, they must have been met with. 

By such thorough-going examination, various inductive laws 
have been established, including that momentous truth called 
the Law of Causation. Now, in whichever of its two properly 
scientific aspects, we view this law— whether in the less sug- 
gestive but perfectly accurate form of Uniformity of Sequence, 
or in the new and better form of Conservation accompanied 
with Collocation, we find in it a means of shortening the labour 
of ascertaining specific causes and effects. By applying the 
general law, in either form, there is often a possibility of prov- 
ing causation by a single instance. 

Thus, to take the first form of Causation— < Every event is 
uniform y followed by some other event; and every event is 
uniformly preceded by one or other of a definite number of 
events :— - given an antecedent, one consequent succeeds ; given 



CAUSATION TIIE BASIS OF ELIMINATION. 

& consequent, some one of a few definite ant. 
ceded. Now from this it follows, that whenever an agent is 
introduced into a quiescent state of things, and .tain 

changes follow at once on that fact, the sequence happening 
once will happen always. Nothing springs out of not) 
Nature in the matter of sequences is uniform; and a si 
case, cleared of ambiguities, establishes a law. By the stroke 
of an axe, a block is cleft ; the same effect will always follow 
-arae cause. Hence, a single experiment in the laboratory 
may establish for ever a casual property. 

On the second or more precise form of Causation, there is 
a definite transfer of motive power under some given an a 
ment of things. We know, by this law, without any new 
observation, that a blow with a hammer will realize its 
equivalent, either in mechanical energy, or in some form 
of molecular force. If in a certain situation, it splinters a 
stone, it will always do the same thing, in the same situation. 
In a different arrangement, it raises the temperature of a 
surface ; and what it does once, it does always. All that we 
have to settle empirically in this form of the law, is the 
transfer attending each collocation, and the collocation attend- 
ing each transfer. By induction proper (universal agree- 
ment) we have already ascertained this to be uniform, and 
accordingly pronounce upon a single clear instance. 

There is thus only one Inductive Method at the foundation 
(Agreement), but there are several Deductive Methods, or 
methods depending upon the grand generalization of Cause. 
For instance, the method known as the * Method of Differ- 
ence,' is not an inductive but a deductive method ; for, with- 
out the law of Causation, the method would be incompetent. 
Even the ' Method of Agreement ' as employed for the pur- 
pose of elimination, supposes the Law of Causation, and is to 
that extent a deductive method. 

6. The Law of Causation involves the three following 
affirmations, each of which is the groundwork of u prt 
of Elimination. 

(1) Whatever antecedent can be left out, without preju- 
dice to the effect, can be no part of the cause. 

A cause is what produces an effect. As the presence of 
the cause is the presence of the effect, so the absence ot the 
cause is the absence of the effect. The absence of the ca 
with the presence of the effect, would be a contradiction of 
the law. We are sure, therefore, that whatever can be omitted 



WEAPONS OF ELIMINATION, 
withdrawn without making any difference to the effect in 






or withdrawn witnout mailing any uiuerenuc tu uie eueut m 
question, is not the cause, or any part of the cause. If we ' 
cat a .string that we suppose to be the support of a weight, 
and the weight continues to be supported, the string is not 
the support. 

in the Law of Causation, viewed on this side, reposes 
Mr. Mill's Method of elimination by Agreement. A certain 
effect remains after the successive withdrawal of all the ante- 
cedents except one; which leaves that one in sole and undis- 
puted possession, and therefore the cause. 

(2) When an antecedent cannot be left out without the 
consequent disappearing, such antecedent must be the 
cause or a part of the cause. 

This affirmation, likewise, is implied in the law. It presents 
the other side of the same linking of cause and effect ; absence 
of the cause is absence of the effect. Whatever, by disappear- 
ing, makes the effect to disappear, is by that very fact an 
essential or causal condition. If the cutting of a string is the 
falling of a weight ; the string is the support of the weight. 

This aspect of cause gives the decisive Method of Difference; 
the method whereby a single instance may be incontrovertible 
proof of a cause. 

(3) An antecedent and a consequent rising and falling 
together in numerical concomitance are to be held as Cause 
and Effect. 

This is Causation in the more special aspect of Conserva- 
tion, and is directly implicated in that principle. In the 
transfer of moving power, the quantity gained is the quantity 
lost ; and the tracing of quantitative concomitance is our very 
be.st clue to the force operative in a given effect. As the com- 
bustion of a locomotive is increased, so is the steam power. 

In those agencies that merely bring about a collocation, 
there is no numerical ratio between the agent and the result. 
A slight touch is enough to complete the electric circuit, and 
a double vehemence adds nothing to the energy of the circuit. 

The process now described is the Method of Concomitant 
Variations. 

These are the three chief methods of Eliminating the nn- 
concerned circumstances present in cause and effect. After 
considerable progress has been made in the discovery of 
causes, recourse may be had to a farther proceeding, namely, 
to allow for the influence of all known causes, and to attribute 






ELIMINATION FOUNDED ON CAUSATION. 



what remains of the effect to what remains of the cause. Thin 
also is a proper inference from the Law of Causation. It is 
termed the Method of Residues. 

The Method of Agreement may be employed negatively; 
that is, cases may be found where cause and effect are uni- 
formly absent together. We may call it Agreement in Ah 
When this circumstance can be conjoined with the positive 
method— Agreement in presence— an approach is made to the 
decisive cogency of the Method of Difference, Mr. Mill lias 
given to this conjoint mode the designation — Joint-Method. 

The following chapter will exemplify the employment of 
these Five Methods of Inductive (or Deductive) Elimination 
in investigating Cause and Effect. 

It is not possible to separate from the thorough working of 
these instruments of Elimination the process of generalizing, 
or attaining to Inductive generalities. In carrying out the 
Method of Agreement, for example, the collation of a large 
number of instances where a cause or an effect is present, 
cannot fail to suggest laws of causation of a higher generality 
than the enquirer sets out with. Nevertheless, it will not be 
expedient to dwell upon this generalizing operation while we 
are bent upon the eliminating process. Generalization belongs 
to Discovery ; Elimination is Proof ; and Proof, more than 
Discovery, is the end of Logic. Still, we shall have to make 
room for a consideration of the best modes of arriving at the 
higher generalities. 



CHAPTER VI. 
THE EXPERIMENTAL METHODS. 

1. There are three chief methods of eliminating the 
cause of a phenomenon from the neutral or indifferent 
accompaniments— Agreement, Difference, and Concomitant 
Variations. 

METHOD OF AGREEMENT. 

2. The Method of Agreement is expressed thus : — If 
two or more instances of a phenomenon under investiga- 

13 

J 



OSO • THE EXPERIMENTAL METHODS. 

tion have only one circumstance in common, that circum- 
stance is the cause (or effect) of the phenomenon. 

The instances are studiously varied so as to leave out m 
turn all the circumstances attending the phenomenon. What- 
ever is left out, in any one instance, without detriment to the 
effect, cannot be the cause ; the possibilities are gradually 
reduced in number ; and, if the means of elimination are com- 
plete, the enquiry terminates in assigning one circumstance 
that has never been wanting where the phenomenon appears. 

The method is illustrated symbolically thns :— Let A repre- 
sent a cause and a an effect. In nature we seldom have A 
followed by a alone ; were such isolation the rule, the Experi- 
mental Methods would be unnecessary. What we find is A in 
combination with other things as A B C, and a also in com- 
bination, as in a & c. But, now, if these conjunctions were 
rigid and invariable, we should have no opening for the 
methods. The real fact is, however, that though a cause may 
be always in combination with other agents, it is not always 
in the same combination ; at one time the union is A B C, at 
another time A B D, and again ACE; there being corres- 
ponding conjunctions in the effects — a b c, a b d y a c e. 
If we suppose, then, the instances — 

ABC giving a b c, 

A B D giving a b d, 

ACE giving ace, 
we reason thus. So far as the first instance is concerned — 
ABC giving a b c, the effect a may be produced by A, or 
by B, or by C. In the second instance — A B D giving a b d, 
the cause C is absent, the effect a still remaining ; hence C is 
not a cause of a. In the third instance — A C E giving ace, 
— B is absent, a remaining ; hence B is not a cause of a. The 
only antecedent persisting through all the instances is A ; 
when a is present as a consequent, A is always present as an 
antecedent. If, then, we are sure that every other antecedent 
circumstance has been removed in turn, the consequent a still 
surviving, we have conclusive evidence that A is a cause, 
condition, or invariable accompaniment of a. 

It matters not which is the form of the enquiry, — given an 
effect to find a cause, or given a cause to find an effect. The 
first is supposed to be the more frequent occurrence. Science, 
from of old, was 

rerum cognoscere causas. 

If the problem be given in the first form, the proof is always 
given in the second ; we try a cause to see what effect 



METHOD OF AGREEMENT. 

will follow, which proves at once that the consequent 
effect of the antecedent, and that the ai 
ot the consequent ; the two affirms 

-hough. our professed object now : 
elimination of Cause ana 
the case of Co-existence as Co-inheri: 
expounding the Methods, we must recei 

iminately, as we do not at first know how they will turn i 
There are many connexions of Cause and Effect fch 
as Co-existences, and there are instances that we most 
undecided, being unable to a e ultimate nature of the 

union. The more obvious tests of Causation are these : 

(1) sequence in time, as when innoculation is the 

small-pox pustule; (2) expenditure of energy, as when a 
cannon ball shatters a fort. Where these tests are wanting, as 
in co-inhering powers of the same substance—: ,le, 

avity and inertia — we are left to presume co-existence, 
ere being, as alternative possibilities, mutual implication, and 
the co-existing effects of a common cause. 

This explanation is more especially called for in commenc- 
ing the Method of Agreement — the universal or fundamental 
mode of proof for all connexions whatever. Under this 
method in particular, we must be ready to admit all kinds of 
conjunctions : reducing them under Causation, when we are 
able, and indicating pure Co-existence when the presumption 
inclines to that mode. 

As a simple example, we may take the case of the c . 
sion of solid bodies into liquids, and the farther conversion of 
liquids into gases. The bodies so converted are of every 
possible variety of properties ; the one circumstance common 
to all the instances of such conversion is the application of 
heat. The elimination is complete as regards this antecedent, 
which is therefore correctly assigned as the essential condition 
or cause. We may apply in this example, the most decided 

t of Causation, the expenditure of energy or force ; we sho 
never regard the fact as a mere Co-existence. 
The next example is of a different character. 
The peculiar phenomenon known as the interference of 
polarized light — consisting in the exhibition of rin^s of alter- 
nating or 'periodical' colours, when a polarized beam cf 
light passes through certain transparent substances — m 
be propounded tor investigation. We m: 

other property or phenomenon always present in the bodies 
that show this peculiar effect ? Now, the bodies must, as a 



THE EXPERIMENTAL METHODS. 

matter of course, be transparent; but all transparent bodies 
do not exhibit the polarized bands; hence, transparency is 
eliminated. By farther comparison of instances, we find that 
there is do constant mode of colour, of weight, of hardness, 
of form (crystalline), of composition (physical or chemical) ; 
so that no "one of all these properties is concerned in the 
phenomenon. There is, however, one property common to 
all the substances that furnish these coloured bands, they are 
all doubly refracting substances, that is, present two images of 
things seen through them obliquely. By Agreement through 
all known substances, there is proof of the concurrence of 
these two properties. 

It is not ascertained, however, and cannot be ascertained by 
Agreement alone, whether the two facts are cause and effect, 
or whether they are a case of co-existence without causation. 
Agreement is the method of proof for all conjunctions what- 
soever — whether Causation or Co-existence. The enquiry 
belongs to a particular class — the conjoined Properties of 
Kinds, where there may be laws of co-existence without cau- 
sation. The decisive criteria of causation are wanting in the 
case. 

To take a third example. In flowers, there is a remark- 
able concurrence between the scarlet colour and the absence 
of fragrance. The following quotation gives a selection of 
instances. 

' Among all the colours that blooms assume, none are less 
associated w T ith fragrance than scarlet. We cannot at present 
recollect a bright scarlet blossom that is sweet-scented — yet 
no other colour among flowers is more admired and sought 
after. Scarlet prevails among Balsamina, Euphorbia, Pelar- 
gonium, Poppy, Salvia, Bouvardia. and Verbena, yet none of 
the scarlets are of sw T eet perfumes. Some of the light-coloured 
Balsams and Verbenas are sweet-scented, but none of the 
scarlets are. The common Sage, with blue blooms, is odorifer- 
ous both in flower and foliage; but the scarlet Salvias are 
devoid of smell. None of the sweet-scented-leaved Pelar- 
goniums have scarlet blooms, and none of the scarlet bloomers 
have sweet scent of leaves nor of blooms. Some of the white- 
margined Poppies have pleasant odours ; but the British 
scarlets are not sweet-scented. The British white-blooming 
Hawthorn is of the most delightful fragrance ; the scarlet- 
flowering has no smell. Some of the Honeysuckles are 
sweetly perfumed, but the Scarlet Trumpet is scentless' (Elder, 
American Gardener's Monthly). 



EXAMPLES OF AGREEMENT. 

Fourth Example. The Norih-East wind is known | 
specially injurious to a great many persons. Del bhe enquiry 
be— what circumstance or quality is this owing bop 
mental analysis, we can distinguish various qaalities in * 
—the degree of violence, the temperature, the huraidi 
dryness, the electricity, and the ozone. We then refer to 
the actual instances to see it' some one mode of any 
qaalities uniformly accompanies this particular wind. 
we find, that as regards violence, easterly winds are generally 
feeble and steady, but on particular occasions, they are stormy ; 
hence, we cannot attribute their noxiousness to the intensity 
of the current. Again, while often cold, they are sometim s 
comparatively warm; and although they are more disagree- 
able when cold, yet they do not lose their character by being 
raised in temperature ; so that the bad feature is not coldness! 
Neither is there one uniform degree of moisture; they are some- 
times wet and sometimes dry. Again, as to electricity, there 
is no constant electric charge connected with them, either 
positive or negative, feeble or intense ; the electric tension of 
the atmosphere generally rises as the temperature falls. 
Farther, as respects ozone, they have undoubtedly less of this 
element than the South- West winds; yet an easterly wind at 
the sea shore has more ozone than a westerly wind in the heart 
of a town. It would thus appear that the depressing effect 
cannot be assigned to any one of these five circumstances. 
When, however, w r e investigate closely the conditions of the 
north easterly current, we find that it blows from the pole 
towards the equator, and is for several thousand miles close 
zipon the surface of the ground ; whereas the south-west wind 
coming from the equator descends upon us from a height. 
Now, in the course of this long contact with the ground, a 
great number of impure elements — gaseous effluvia, tine dust, 
microscopic germs — may be caught up and may remain sus- 
pended in the lower stratum breathed by us. On this point 
alone, so far as we can at present discover, the agreement is 
constant and uniform. 

What is the conclusion ? As Agreement by itself docs not 
decide that conjoined circumstances are cause and effect, we 
must find some mode of excluding Co-existence, and rendering 
the case one of succession. When the two c renrastances are 
plainly in succession, as when a fracture follows a blow, uni- 
form agreement (with elimination) proves causation ; when 
they are not demonstrably successive, the agreement fails in 
this respect. 



2 Si THE EXPERIMENTAL METHODS. 

Now, there is a general belief that the two events supposed 
—the oust wind and the uncomfortable sensations — are not 
contemporaneous, but in succession; the wind first, the feel- 
ings afterwards. This belief is supported by the circumstance 
that a change of feelings, must have, according to the law of 
Causation, an antecedent condition; and if all antecedents, 
besides the one above named, are eliminated, that one is the 
cause, or an essential part of the cause. 

The phenomenon to be explained is not a permanent fact 
or potentiality, like polarization or double refraction, it is a 
temporary manifestation, and requires some causal circum- 
stance to bring it forth. In this respect, it resembles the 
actual display of one of these optical properties ; it cannot 
happen without a suitable agent and collocation, which is pro- 
perly a cause of the appearance. 

If then, the elimination be supposed complete, there is a 
proof by Agreement that the deleterious influence of the east 
wind is due to the circumstance named ; and the case exempli- 
fies the eliminating efficacy of the method. 

In the foregoing example, we cannot withhold from our 
mind a certain -presumption in favour of the result, grounded 
on our knowledge of the deleterious tendency of atmosphere 
imparities caught up from the surface of the ground. This 
is a circumstance not properly belonging to the proof by 
Agreement; it is a confirmation from deductive sources. The 
addition of such a presumption always operates strongly on 
our belief ; the total absence of it leaves a considerable shade 
of uncertainty in all the methods, but most of all in Agree- 
ment. The third example shows this deficiency ; we are not 
at present aware of any connexion of a causal kind between 
the scarlet colour of flowers and the absence of fragrant 
odour ; the proof of the law rests upon the Agreement alone. 
That method of proof is final, only when the elimination has been 
exhausted, by variation of circumstances, and when the coin- 
cidence has been shown through all nature, so as to establish 
a law of Universal Co-existence. 

Fii fch Example. Let the phenomenon given be Crystallization, 
and let the thing sought be the antecedent circumstances, 
positive and negative, of the formation of crystals. This is a 
case of succession, and therefore of Causation. 

We must begin by collecting instances of the effect. In the 
following series, the circumstances are purposely varied with 
a view to elimination : — ' 

1. Freezing of water. 



EXAMPLES OF AGREEMENT. 






2. Cooling and solidifying of molten metals and niiner.il>. 

3. Deposition of salts from eolations, 

4. Volatilizing of solutions. 

5. Deposition of solids from the gaseous styte, as iodine. 
G. Pressure. 

7. Slow internal change, as in rocks. 

8. The transformation of metals from the tongh to the 

brittle condition, by hammering, vibration, an 
peated heatings and coolings. 

Looking at the first and second instances— ice, and the 
solidifying of molten metal — we discover two antecedent eir- 
cumstances, namely, lowering of temperature, aud change 
from the liquid to the solid state. 

The third instance — deposition of salts from solution — 
agrees in the same two circumstances, there is a lowering of 
temperature, and also a change from liquid to solid. 

The fourth instance — the volatilizing of solutions, as in 
boiling down sea-water — appears to fail in the matter of cool- 
ing, but still contains the circumstance of prior liquidity ; the 
prominent fact is that the solvent is driven off, and the dis- 
solved substance thereby compelled to resume the solid state. 

The fifth instance — the deposition of solids at once from 
the gaseous state, as in the case of iodine— seems to eliminate 
prior liquidity. We must then shift the ground, and, for 
liquidity, substitute one of the two higher states of matter. 

The sixth instance is * heavy and long continued pressure 
upon an amorphous substance ; ' principally shown in geology. 
This would eliminate the prior liquid or gaseous condition, and 
bring to view the forced approximation of the constituent 
particles of bodies. But the same circumstance accompanies 
all the previous cases, being merely a different expression of 
what is common to them. We know heat as forcibly enlarg- 
ing the bulk of bodies — making their particles mutually re- 
pellent ; the withdrawal of this force leaves the attractions of 
the particles free to operate. 

The seventh instance — slow geological transformation — 
unless viewed by the light of the circumstance just named, is 
difficult to interpret. It is not, however, incompatible with 
the predominance of the molecular attractive lorces by the 
abatement of the repellent forces. 

The eighth instance — change of metals from the tcagh to 
the brittle state — is a true case of crystallization ; brittle - 
ness is accompanied with an imperfect crystalline arrangemeut. 
The effect is produced by cooling after hammering ; by re- 



2SG THE EXPERIMENTAL METHODS. 

peatcd beating and cooling ; by long-continned vibration or 
concussion :— all which influences tend to expel the structural 
of the substance; the consequence being that the mole- 
cular attraction is more preponderant. 

We have thus eliminated Cooling, Deposition from Solution, 
and Prior Liquidity ; and have found but one uniform antece- 
dent — the increased scope and operation of the molecular or 
solid-forming cohesion; to which point, however, these other 
circumstances really tend ; they are all of them remoter ante- 
cedents of the one constant antecedent. The examination of 
the instances has enabled us to generalize the phenomenon, as 
well as to establish the generality upon evidence, namely, the 
evidence of Agreement. 

As we have stated this enquiry, it is a clear case of Cause 
and Effect. We have sought the antecedent circumstances 
whereby a body in an amorphous or un crystallized state be- 
comes crystallized ; and we find that there is an expenditure 
and re-distribution of power or energy. The result of the ex- 
penditure is not an active manifestation, as when we produced 
mechanical force, or heat ; it is an arrangement, or structural 
collocation ; a case already contemplated (p. 265) among the 
results of expended force. 

Sixth Example. Let us next apply the method to eliminate 
the cause, or the antecedent conditions essential to the pro- 
duction and maintenance, of Light. 

Now, the most constant circumstance is a high temperature ; 
solid bodies become luminous at a temperature of from 980° 
to 1000° Fahrenheit. So far, there is a remarkable unanimity. 
It is found, however, that gases do not always become lumin- 
ous at this temperature, nor at a much higher ; a current of 
gas ^ may be raised to upwards of 2000° F. without being 
luminous ; whence we conclude that the state of the body is 
also a condition. Again, the electric spark is a luminous 
effect, which would give the disturbance of the electric 
discharge as an antecedent. As there is a possibility, however, 
I hat the great violence of the discharge may be accompanied 
with sudden rise of temperature, this may be merely another 
lorm of heat. We should need to show, by varying the 
instances, that high temperature is not essential to the spark. 
In the next place, certain substances give light at common 
temperatures, to which fact has been given the name phosphor- 
escence. Some minerals, gently heated, emit a feeble light, 
which soon ceases, and cannot be renewed until the body has 
been exposed to the sun or the electric spark. This is still a 



COGENCY OF AGREEMENT. 

form of heat, but not of the intense degree of ordinary 1 
More peculiar still is animal phosphorescence, as the glow- 
worm, tire-fly, and certain sea animalcules. Here the accom- 
paniment is a special mode of vitality hitherto urieliminated, 
and excluding the circumstance of high temperature (Mr, 
Herbert Spencer suggests that it is an incident attending 
oxidation). Once more, a faint Hash of light occurs wi;h 
certain substances in the act of crystallizing. 

We may thus collect from Agreement, that ignited solids at 
the temperature of 1000° are luminous, and that an electrio 
discharge is luminous; but we cannot at present lay down 
any wider generalization. Excepting the very general fact of 
molecular disturbance of some kind or other, which we are 
unable to qualify in the precise mode concerned in the effect, 
our comparison of instances does not point to a constant 
circumstance. For the present, we regard Light as having 
a plurality of causes. 

As farther instances of Agreement, we may quote the proof 
of the coincidence of Sleep with low nervous action, which 
means a feeble cerebral circulation ; also, the connexion of 
Memory with the intensity of Present Consciousness. The 
uniformity of these conjunctions under all varieties of other 
conditions is the evidence afforded by Agreement. The Rela- 
tivity of Knowledge is established partly by Agreement, partly 
by the method of Concomitant Variations, as will be shown. 

The cogency of Agreement is manifestly in proportion to 
the thoroughness of the elimination. Whatever circumstance 
has never been eliminated is a possible cause. There are not 
a few instances, as in the action of drugs, where nature does 
not provide the variety requisite for a thorough elimination. 
The complicacy of the Natural Kinds passes our means of 
extrication by Agreement alone. 

METHOD OF DIFFERENCE. 

3. Elimination by Difference is expressed in the follow- 
ing canon : — If an instance where a phenomenon occurs, 
and an instance where it does not occur, have every cir- 
cumstance in common except one, that one occurring only 
in the first ; the circumstance present in the first and 
absent in the second, is the cause, or a part of the cause, 
of the given phenomenon. 

We are supposed to have two instances and only two. Each 
is a complex sequence, a group of antecedents followed by a 



9gS THE EXPERIMENTAL METHODS. 

K roup of consequents. The two complex sequences differ by 
only a single sequence, present in the one, and absent in the 
other. Thus the sequence A B C D gives abed, and BCD 
\ b c d: the only difference being the presence of A in the 
antecedent, and of a in the consequent, of one sequence, and 
the absence of these in the other sequence. Supposing A B C D 
changed into B C D, by the loss of A; while at the mom- 
ent a b c d is changed into b c d by the loss of a ; we have 
a proof of the connexion of A with a. Indeed, the assertions 
are identical ; to say that the disappearance of one thing is 
followed by the disappearance of another thing, there being no 
other change, is merely a way of expressing causal connexion. 

Difference plays a great part in our everyday inferences. 
The usual form is the sudden introduction of some limited and 
definite agency or change, followed by an equally definite con- 
sequence. When the drinking of water is followed at once by 
the cessation of thirst, we do not hesitate to pronounce the one 
fact the cause of the other. The human system is a great 
complication, but the only difference made upon it in two 
successive minutes is the sequence of drinking and the satisfy- 
ing of thirst ; there has been, we presume, no time for any 
other change to manifest itself. So when we waken a sleeper 
by a noise, or strike a light by the friction of a match, we 
infer causation ; the new agency being instantaneously fol- 
lowed by the new effect. 

The first example given, under Agreement, is also proved by 
Difference. That Heat is the cause of the melting of ice, of 
wax, or of lead, is proved by making, upon these substances, 
the one change of raising the temperature. Being quite sure 
that in the conversion of ice into water, no change has been 
made except this, we have a conclusive experiment of Differ- 
ence to show that heat is the cause. 

The same substance in two states, as solid and liquid, or a3 
amorphous and crystallized, enables us to ascertain what effects 
are due to change of state. Thus charcoal, uncrystallized, is 
black, opaque, and a conductor of electricity ; as crystallized, 
in the Diamond, it is transparent and a non-conductor. 

A large part of our knowledge of nature and of living beings 
is gained by making experimental changes and watching the 
consequences. Our proof is the immediate result. An im- 
mediate response is satisfactory evidence in almost any de- 
partment. Thus, in medicine, there is little doubt as to the 
operative force of purgatives, emetics, sudorifics, diuretics, 
narcotics, stimulants, irritants; the uncertainty attaches to 



METHOD OF DIFFERENCE. 

alteratives, tonics, and the protracted treatment of chronic 
cases. The effect of quinine, in ague, is established Lk 
dispute. 

Whether it be to add, or to withdraw, a definite agent, a 
change instantly following is proved to be an effect. Even in 
politics, we may have a proof from difference; as in the 
accession or resignation of a minister, like Chatham. Ko 
other circumstances arising in the ordinary course of a year 
would make that total change in the course of politics that 
followed on Chatham's becoming minister. It could not be 
denied that he was the cause (in the practical sense of cause) 
of our successes in America, and on the continent of Europe. 
The consequences of his retirement were equally decided as 
proving, on the method of Difference, the vast superiority of 
his powers as an administrator. 

Wherever Difference can be resorted to, the knowledge of 
causes is gained at once. In ordinary cases, the method is so 
obvious in its application, so satisfactory and conclusive, as 
scarcely to need a master to explain or enforce it. The special 
discipline of Logic, so far as this method is concerned, lies in 
showing the precautions requisite in the more complicated 
cases. 

In Physiology, the functions of the nerves were ascertained 
by the experiment of dividing each in turn, and watching the 
effect. Whatever function is immediately arrested on the 
division of a nerve, is shown to be due to that nerve, or to 
require that nerve in order to its performance. Such experi- 
ments, however, do not exhibit the entire circle of conditions 
involved in the function in question. We know that the 
integrity of the spinal cord is necessary to sensation and to 
movement in the trunk and in the extremities of the body ; 
we do not exhaustively know what else is necessary. For this 
more extensive knowledge we should have to multiply experi- 
ments all through the brain. If the destruction of any part 
interferes with these functions, that part enters into the 
causal conditions ; if otherwise, it does not enter into those 
conditions. 

The extension of this class of experiments to the brain 
exemplifies one situation where the method of Difference may 
be indecisive. Deep incisions in the brain, intended to affect 
one single organ, as the cerebellum, may injure adjoining 
organs ; and may therefore be inconclusive as to the functions 
of the special organ in view. It is on this ground that 
Brown-Sequard objects to the views of Flourens regarding the 



290 T I TE EXPERIMENTAL METHODS. 

function of the cerebellum. The one certain inference in such 
capes is, that whatever function survives, in its integrity, the 
destruction of an organ, cannot be exclusively due to that 

ran. The obverse inference is certain only on the supposi- 
tion that the injury has been confined to the part affected. 

With reference to the connexion of scarlet bloom with 
absence of odour, we have a seeming case of Difference in 
comparing such varieties as the white-flowering and the red- 
flowerin ^hawthorn : the one fragrant, the other not. In the 
complicacy of Kinds, we can seldom be sure that a variation 
is rigidly confined to the circumstances that are apparent. 
Moreover, where there is not a clear case of Causation, Differ- 
ence is insufficient to prove a coincidence. 

Sir G. C. Lewis lays it down as essential to the validity of 
a proof by Difference* that we should know, by a previous 
induction, the general adequacy of the assigned cause to the 
production of the effect. When w r e infer that a man, shot 
through the heart, drops down dead, we need to know, he 
thinks, that, as a general rule, a gunshot wonnd in the heart, 
is a cause of death. To this remark the reply is, that practi- 
cally we do make use of such previous knowledge, but it is 
not essential to the method of Difference. Provided we are 
quite sure that the new agent is the only change that has 
preceded the effect, the instance is conclusive, on the Law of 
Causation solely. The use of a more specific induction is to 
supply the defect of certainty in the instance itself. There 
may be other unseen agencies at work, as well as the one 
supposed, and this is the only ground either for invoking a 
general presumption, or for multiplying instances of the 
phenomenon. In practice, we seek both for presumptions 
(from prior inductions) and for repetition of instances ; but 
an ideally perfect instance of Difference, in a case of Causation, 
is conclusive in itself. 

Agreement and Difference can be easily compared as to their 
respective advantages and disadvantages. Agreement needs 
a large number of instances, but their character is not re- 
stricted. Any instance that omits a single antecedent contri- 
butes to the result ; the repetition of the same instance is of use 
only as giving means of selection. Difference requires only 
one instance ; but that one is peculiar, and rarely to be found. 

A great extension is given to the power of Agreement, by 
extending it to agreement in absence. When such cases are 



JOINT METHOD. go.] 

conjoined witli those where the agreement is in presence, there 
is an approach to the conclusiveness of the method of Differ- 
brace. This double employment of the method of Agreement 
is brought forward by Mr. Mill under the designations-~tbe 
4 Joint Method of Agreement and Difference, 1 andthe 'Indirect 
Method of Difference.' It might also be called the 'Method 
of Double Agreement/ 

JOINT METHOD. 

4. The canon of this Method is : — If two or more in- 
stances where the phenomenon occurs have only one cir- 
cumstance in common, while two or more instances where; 
it does not occur have nothing in common save the absence 
of that one circumstance ; the circumstance wherein alone 
the two sets of instances differ, is the effect, or the cause, 
or a necessary part of the cause of the phenomenon. 

If we require to ascertain, under this method, that A is 
the cause of a, or a the effect of A, we add, to the instances of 
uniform presence of A and a, other instances of uniform 
absence, as B F G followed by. b f g, C H I followed by c h i, 
and so on. If we have never discovered A wanting as an 
antecedent without having a absent as a consequent, there is 
a strong additional presumption that A and a are united as 
cause and effect — a presumption that may approach to the 
certainty of the method of Difference. 

It is a confirmation of the cause, suggested by Agreement, 
of the noxiousness of the North-East wind, that the South- 
West wind, the genial and wholesome current, is wanting in 
the circumstance assigned. It descends upon us from the 
eleyated regions of the atmosphere, where impurities are 
highly diluted by dissemination. 

Again, to revert to the example of Crystallization. Let us 
review the non-crystallized solids, and note the mode of 
their formation. The amorphous stones and rocks, as sand- 
stone, chalk, &c, are known to be sedimentary deposits from 
water. Before being solidified, they existed as solid particles ; 
they were not dissolved in water, neither did they exist in a 
molten condition. This Agreement in absence would confirm 
the inference from Agreement in presence — that (so far as 
certain instances went) crystals existed in a previous higher 
condition. But the general inference, from the full compari- 
son of examples, was the superior play given to the molecular 
attraction by counterworking the molecular repulsion. Now, 



292 THE EXPERIMENTAL METHODS. 

this general fact is absent from all mere sedimentary deposits; 
these bodies have no aid, in the shape of loss of heat or other 
cause, to their molecular attractions. 

The comparison of the amorphous rocks yields another 
circumstance, namely, the irregular mixture of different sub- 
stances. For, although in a mud sediment silica or alumina 
may prevail, neither is ever pure ; and the mixture of different 
elements is a bar to crystallization, unless they are of the 
kind called isomeric (from crystallizing alike). There is more 
to be got over in crystallizing compounds of unlike elements, 
and the crystals must be deficient in regularity. 

Another un crystallized class comprizes the vegetable and 
animal tissues. In their case, however, the antecedent circum- 
stances are too complicated and obscure to furnish insight; 
they rather stand in want of illustration by the parallel lights 
of more obvious cases. Besides, there is in them a method 
and order of aggregation more analogous to the crystallized, 
than to the amorphous solid.s. 

A third class includes the Colloids, or glue-bodies, of 
Graham (represented by gum, starch, gelatin, albumen, tannin, 
caramel). They are not confined to the viscid form of glue,, 
but include compact solids, as flint. The points of contrast 
between these and crystallized bodies are numerous and 
important. Their mode of formation is various ; many of 
them are the products of living bodies, and therefore share in 
the complication of living growth. Mint is. an aggregate of 
particles of silica, which particles were originally the shells of 
animals, and therefore also organic in their formation. In 
this case, the molecular attraction of silica, in its progress 
towards crystallization, is thwarted by the pre-existing forms 
of the silicious particles. 

It would require too long a discussion to show the bearing 
of the colloid peculiarities on the question as to the antece- 
dents of the crystalline formation. Enough has been given to 
show the working of the method of Obverse Agreement. 

METHOD OF CONCOMITANT VARIATIONS. 

5. Canon of the Method : — Whatever phenomenon 
varies in any manner whenever another phenomenon 
varies in some particular manner, is either a cause or an 
effect of that phenomenon, or is connected with it through 
some bond of concomitance. 

Tho effects of Heat are known only through proportionate 



CONCOMITANT VAR1ATK 

variation. We cannot deprive a body of all its 1 cv 
nature o? the agency forbids us. But," by i 
the amount, we ascertain concomitant changes in t. 
panying circumstances, and bo can establish 

thus that we arrive at the law of the expansion of b 
by heat. In the same way, we prove the equivalence ot 
and Mechanical Force as a branch of the great law 
servation or Persistence of Force. 

The proof of the First Law of Motion, as given by Nov. 
assumed the form of Concomitant Variations. On the < 
there is no instance of motion persisting indefinitely. lu 
proportion, however, as the known obstructions to motion — 
friction and resistance of the air — are abated, the motion of a 
body is prolonged. A wheel spinning in an exhausted receiver 
upon a smooth axle runs a very long time. In Borda'fl experi- 
ment with the pendulum, the swing was prolonged to more 
than thirty hours, by diminishing friction and exhausting the 
air. Xow, comparing the whole series of cases, from speedy 
exhaustion of movement to prolonged continuance, we find 
that there is a strict concomitance between the degree of 
obstruction and the arrest ; we hence infer that if obstruction 
were entirely absent, motion would be perpetual. 

The celebrated experiment of carrying the barometer to the 
top of Pay de Dome was a proof by variation of the connexion 
between the pressure of the air and the rise of the mercury. 

By Concomitant Variations, we derive one of the proofs of 
the connexion between the brain and the mind. In the same 
manner, we learn to associate health with the healthy agencies, 
and diseases with noxious agencies. 

The doctrine that change of impression is an essential con- 
dition of consciousness, from which proceeds the theory of 
Relativity as applied to feeling and to knowledge, is most 
strikingly attested by Concomitant Variations. The intensity 
of a mental impression notably varies according to the greatness 
of the transition from one state to another : witness the in- 
fluence of novelty, of all great changes of circumstances, of 
suddenness and surprise. 

The Statistics of Crime, reveal causes by the method of 
Variations. When we find crimes diminishing accordi: 
labour is abundant, according as habits of sobriety have in- 
creased, according to the multiplication of the means of 
detection, or according to the system of punishments, we may 
presume a causal connexion, in circumstances not admitting 
of tho method of Difference. 



0Q4- THE EXPERIMENTAL METHODS. 

The Concomitance may be inverse. Thus we find that the 
tendency to chemical action between two substances increases 
as their cohesion is diminished, being much greater between 
liquids than between solids. So, the greater the elevation of 
the land, the less the temperature, and the more scanty the 
vegetation. 

Parallel Variation is sometimes interrupted by critical 
points, as in the expansion of bodies by heat, which suffers a 
reverse near the point of freezing. Again, the energy of a solu- 
tion does not always follow the strength ; very dilute solutions 
occasionally exercise a specific power, not possessed in any 
degree by stronger. So, in the animal body, food and stimu- 
lants operate proportionally up to a certain point, at which 
their farther operation is checked by the peculiarities in the 
structure of the living organs. 

The properties of highly rarefied gases do not exhibit an 
exact continuity of the phenomena that vary with density. In 
a perfect vacuum, there is no electrical discharge ; but the 
variations of the discharge, in highly rarefied air, do not pro- 
ceed in exact accordance with the degree of rarefaction. 

We cannot always reason from a few steps in a series to the 
whole series, partly because of the occurrence of critical points, 
and partly from the development at the extremes of new and 
unsuspected powers. Sir John Herschel remarks, that until 
very recently ' the formulas empirically deduced for the elas- 
ticity of steam, those for the resistance of fluids, and on other 
similar subjects, have almost invariably failed to support the 
theoretical structures that have been erected upon them.' 

The method of Concomitant Variations is powerful in 
suggesting, as well as efficacious in proving, causal connexions. 
The mind is apt to be aroused to the bond between two 
circumstances by encountering several conjunctions of the 
two in unequal degrees. Very often, we are not alive to a 
connexion of cause and effect till an unusual manifestation of 
the one is accompanied with an unusual manifestation of the 
other. We may be using some hurtful article of food for a 
length of time unknowingly; the discovery is made by an 
accidental increase of quantity occurring with an aggravation 
of some painful sensation. This is one form of the efficacy of 
an Extreme Case; an efficacy felt both in science and in 
rhetoric. 

A remarkable case of Concomitant Variations is furnished by 
the^ discovery of a connexion between the solar spots and the 
positions of the planets. Thus, as regards Venus, 'spots are 



CONTINUOUS COMPARISON. 

nearest to the solar equator when the holio 
of Venus is 0°,' and obversely. 

An important device for discovering, and also for proi 
laws of causation, consists in arranging things 
common property in a serial order, according to 
the property. Thus, we may arrange bodies accordii 
their Transparency or Opacity, according to Specific Grai 
to Conduction of Heat and Electricity, and so on. \\'< 
then in a position to detect any corresponding in 
some accompanying property, and thereby to establish a law of 
concomitance or causation. This method is designated, by 
Mr. Mill, Classification by Series, and by Sir G. C. Lewis, 
the Method of Continuous Comparison. The progress of Life 
in the animal scale ; the progress of mental development in 
human beings ; the progress of civilized institutions, as 
Government, Judicature, the Representative System, — maybe 
expressed in a series, so as to trace concomitant variations. 

It is greatly to be desired that, in Physical Science, all the 
substances in Nature should be set forth in distinct tabula- 
tions, according to the degree of every important property. 
It was when transparent bodies were arranged in the order of 
their refracting power, that the connexion was discovered 
between high refracting power and combustibility. 

METHOD OF RESIDUES. 

6. The canon of Eesidues is : — Subduct from any 
phenomenon such part as previous induction has shown 
to be the effect of certain antecedents, and the residue of 
the phenomenon is the effect of the remaining antecedents. 

After a certain progress is made in the inductive determina- 
tion of Causes, new problems are greatly simplified by sub- 
ducting from a complex sequence, the influence of known 
causes. Sometimes this of itself may amount to a complete 
elimination Such procedure is styled the Method of Residues. 
It is an instrument of Discovery as well as of Proof. 

The method is symbolically illustrated thus : — Suppose tho 
antecedents A B C followed by the consequents a b c; and 
that by previous inductions, we have ascertained that 1> gives 
fc, and C gives c. Then by subtraction, we find A to be the 
cause of a. The operation is substantially the method of Dif- 
ference, and has all the decisiveness belonging to that method. 

Sir John Herschel was the first to show the importance of 
studying residual phenomena. His examples .are very strik- 



290 THE EXPERIMENTAL METHODS. 

ing (Introduction to Natural Philosophy, p. 156). Thus, 
the retardation of the comet of Encke has been the means of 
sn ^o-esting, and may ultimately suffice to prove, the existence 
B resisting medium diffused throughout space. Again, the 
ervation of Arago — tbat a magnetic needle, seta vibrating, 
is sooner brought to rest when suspended over a plate of copper 
— was the first clue to the discovery of Magneto-Electricity. 

The anomalies in the motion of Uranus led Adams and Le 
Verrier to the discovery of Neptune. 

The study of the electrical odour was the first step to the 
discovery of the remarkable substance — Ozone. 

Sir G. C. Lewis remarks that * the unforeseen effects of 
changes in legislation, or of improvements in the useful arts, 
may often be discerned by the Method of Residues. In 
comparing statistical accounts, for example, or other registers 
of facts, for a series of years, we perceive at a certain period 
an altered state of circumstances, which is unexplained by the 
ordinary course of events, but which must have some cause. 
For this residuary / phenome?wn 1 we seek an explanation until it 
is furnished by the incidental operation of some collateral 
cause. For example, on comparing the accounts of live cattle 
and sheep annually sold in Smithfield market for some years 
past, it appears that there is a large increase in cattle, while 
the sheep are nearly stationary. The consumption of meat in 
London may be presumed to have increased, at least in pro- 
portion to the increase of its population; and there is no 
reason for supposing that the consumption of beef has increased 
faster than that of mutton. There is, therefore, a residuary 
phenomenon, viz., the stationary numbers of the sheep sold 
in Smithfield — for which we have to find a cause. This cause 
is the increased transport of dead meat to the metropolis, 
owing to steam navigation and railways, and the greater 
convenience of sending mutton than beef in a slaughtered 
state/ 

The question as to the existence of a special force of Vitality — 
the vital force, or the vital principle — takes the form of an 
enquiry into a residuum. We have first to make allowance 
for the operation of all the known forces of inorganic matter ; 
and when these have been exhaustively computed, the re- 
mainder may be set down to a special influence, or vital 
principle. For anything we know at present, the inoryanic 
forces, operating in the special collocations of organized bodies, 
may be competent to produce all the observed effects. 

The only proof of an exhaustive Analysis, whether in 






PROOF OF AN ANALYSIS BY RESIDUES. 

■ material actions or in mental processes, is there being nothing 
left. Thus, in the Human Mind, it is dispnted whether there 

be a separate and unique faculty, called the .Moral Facuh 
the Moral Sense. Now, there can be no donbt as to' 'the 
presence of common elements of Feeling, Will, and Thought, in 
our moral judgments and actions ; as, 1 in the ease of the vital 
principle, the question is, what remains, when these an 
allowed for. The same application of the .Method of Residues 
occurs in the controversy as to Instincts, and Innate Ideas; 
does Experience, concurring with the usually admitted intel- 
lectual Powers, account for the whole of the facts ? 



CHAPTER VII. 

EXAMPLES OF THE METHODS. 

The Experimental Methods have been regarded mainly as 
instruments of Elimination and Proof, or of separating irrele- 
vant accompaniments from causal accompaniments. In their 
working, however, they unavoidably lead to inductive generali- 
zations, in which aspect they are methods of Discovery. The 
same search for instances, the same comparison of them when 
found, both conduct us to new principles or laws, and prove 
them when once attained. Still, it was not desirable to keep 
np the double illustration throughout. In the miscellaneous 
examples that are to follow, occasional allusion will be made 
to the procedure suited to the discovery of generalities. 

The proofs adduced to show that the mode of action, in 
Smelling, is Oxidation, may be quoted in illustration of the 
Methods. The phenomenon is one of great interest, and of 
some perplexity. The following important facts were indicated 
by Graham. 

The sweet odours are due to hydro-carbons, as the ethers, 
alcohol, and the aromatic perfumes. Now, all these sabsta 
are highly oxidizable at common temperatures, being speedily 
decomposed in the air. Again, sulphuretted hydrogen, the 
most familiar of malodorous substances, is readily oxidized, 
and is destroyed in that manner. These are instances of 
Agreement (in presence). 



29S EXAMPLES OF THE EXPERIMENTAL METHODS. 

A farther instance of Agreement is shown in the decomposi- 
tion of hydrogen compounds, in the act of causing smell. 
When a small quantity of seleniuretted hydrogen is inhaled 
b)' the nose, the metallic selenium is found reduced upon the 
lining membrane of the cavities. The sensation is an intensely 
bad smell. 

A remarkable case of Agreement in Absence is furnished by 
the marsh gas — carburetted hydrogen. This gas has no smell. 
As the proof of the concurring absence of its oxidation at com- 
mon temperatures, Graham obtained it from the deep mines 
where it existed, for geological ages, in contact with oxygen. 
Again, hydrogen itself, if obtained in purity, has no smell ; and 
it does not combine with oxygen at the usual temperature of 
the air. 

An instance approaching to Difference is the following. If 
oxygen is excluded from the cavities of the nose, there is no 
smell. Also, a current of carbonic acid arrests the odour ; an 
influence which may (although not with absolute certainty) 
be supposed hostile to oxidation. 

To make the evidence complete, it is requisite that all the 
instances of the effect should be of the same unvarying tenor, or 
that there should be no exceptions. Until every apparent dis- 
crepancy is reconciled, the facts are inconclusive. A seeming 
exception is the pungency of ozone, which is looked upon as a 
more active form of oxygen. Xow we can hardly suppose that 
ozone combines with oxygen ; a more likely supposition is 
that, by its superior activity, it combines with the nasal mucus. 

The research into the cause of Dew has been used by Sir 
John Ilerscbel, and again by Mr. Mill, as a happy example of 
experimental elimination involving nearly the whole of the 
methods. All the stages of this inductive determination are 
highly instructive. 

The first point is to settle precisely the phenomenon to be 
explained. This is an exercise of Definition, and can never be 
too rigidly attended to. There is some danger, in the present 
case, of confounding the effect with certain other effects ; and 
hence the expediency of defining by an exhaustive contrast. 
H ell, Dew is moisture ; but that moisture is not rain, and not 
fog or mist ; it is moisture spontaneously appearing on the 
surface of bodies when there is no visible wetness in the air. 
In a perlectly clear and cloudless night, there may be a copious 
moisture on the surface of the ground, and this moisture is the 
thing to be accounted for. 



RESEAKCII ON DEW. 

Now, the problem being given as an effect, with the cause 
unknown, we cannot make experiments, until a can 
gested. This is a pure effort of Discovery, preparatory to the- 
application of the methods of inductive proof. On the various 
occasions when dew appears, we must look out for the B 
dant circumstances, with a view to their successive elimination. 
We know, for example, that dew appears chiefly at night, 
which would suggest some of the circumstances conn 
with night-fall, as darkness, cold, and any of the concomitants 
of these. That darkness is not the cause could be shown if 
either dew appears before sunset, or if it ever fails to appear 
at night. As the last alternative is very frequent, we must, 
so far as the Experimental Methods are concerned, pronounce 
against darkness. There would then remain the a^encv of 
Cold. ° J 

Farther, in this preliminary stage of looking out for a pos- 
sible cause, we need not confine ourselves to the actual pheno- 
menon. In the conduct of the research, as recorded, much 
stress was laid upon the reference to analogous effects, or to 
other cases where moisture spontaneously appears on surfaces, 
in the absence of visible wet. All such analogies are valuable 
for suggestion or discovery, in the first instance, and for proof 
afterwards. They are these : — (1) the moisture that gathers 
on cold stone or metal when breathed upon ; (2) the moisture 
on the outside of a tumbler of spring water fresh from the 
well in hot weather ; (3) the moisture that often appears on 
glasses when brought into a hot room full of people ; (4) 
what appears on the inside of windows when a room is 
crowded, and during changes in the outside temperature ; (5) 
what runs down our walls, especially outer passages, when a 
warm moist thaw succeeds to frost. All these cases correspond 
to the definition ; and their comparison is likely to indicate 
some circumstance to be subjected to experimental elimination. 
To take the first instance — the breath upon a cold metallic sur- 
face ; the warmth of the air and the coldness of the surface 
are obvious accompaniments. Some of the others would sug- 
gest the same conjunction, while all are compatible with it. 
Now, this is the situation already suggested by the original 
phenomenon, the dew at night-fall. Consequently, we are in 
a position to proceed experimentally ; we can try the cooling 
down of surfaces under variation of circumstances. 

An easy experiment will tell us whether the cooling of the 
surface be a uniform fact, in the production of dew. Lay a 
thermometer on the dewed grass, hanging another in the air; 



300 EXAMPLES OF THE EXPEKIMENTAL METHODS. 

and repeat this on many successive nights. The actual result 
is that whenever a surface is dewed, it is colder than the air 
around it. This is a proof from Agreement ; but proofs from 
. anient, unless they can be multiplied through all nature, 
in all climes, seasons, and situations, will not of themselves 
decide either causation, or universal coincidence. 

By varying the circumstances, we can bring to bear the 
other methods. We may, for example, try Agreement in 
Absence ; that is, make the same appeal to experiment in 
nights where there is no dew anywhere. The phenomenon, 
however, would be found to evade this test ; there would be 
cases of actual cooling of surfaces below the temperature of 
the air, and yet without dew. Hence the necessity of a dif- 
ferent course of proceeding. 

Observation reveals to us the fact that on the same night, 
and in the same spot, some surfaces are dewed, and others 
not. This holds out the prospect of an appeal to the Method 
of Difference. On the surface of a plate of glass, there may be 
dew, while on a polished metallic surface, there is none. Unfor- 
tunately, however, such a couple is not suited to the canon of 
Difference. The points of diversity between glass and metal 
are too numerous to comply with the stringent requisite of that 
canon. We must, therefore, shift our ground once more. 

It being apparent that the nature of the material enters 
into the effect, let us expose a great variety of different 
materials — metals, glass, stone, wood, cloth, &c. We now 
find that there is a scale of degree ; between the extremes of 
no dew and copious dew, there is a gradation of amount. The 
enquiry then arises, is there any other property of these 
different materials varying in concomitance with their being 
dewed ? Does their temperature (which is the clue that we 
are going upon) change in exact accordance with the amount 
of dew ? There was here scope for a direct appeal to the 
thermometer. We have not, however, to record the issue of 
such an appeal ; the history of the research pursues another 
and more circuitous route for arriving at the conclusion. It 
so happened, that the experiments, begun by Sir John Leslie, 
upon the conduction and the radiation of heat, came in to the 
aid of the present enquiry ; and the use made of these is 
sufficiently illustrative of the canons of Elimination. It 
appeared, on the comparison of the various materials, that the 
rate of becoming dewed varies inversely with the conducting 
power of the substance ; the good conductors— the metals- 
are not dewed, the bad conductors are dewed according to 



RESEARCH ON DEW. 

their badness as conductors. This is the method of Conoomip 
tant Variations ; what it points to will be Been presently. 

It is next desired to ascertain how far difference oi 
operates, material being the same. The comparison shows 
that rough surfaces are more dewed than smooth, and blaok 
more than white. Instead of the direct test of the thei 
meter, the appeal here also is to Leslie's experiments on the 
radiation of heat from surfaces ; those surfaces that are most 
dewed — rough and black—are the best radiators of heat. The 
interpretation of this will be taken with the foregoing. 

In the meantime, make another variation, namely, for texture; 
compare the compact textures of metal, stone, wood, velvet, eid< t- 
down, cotton, &c. ; the compact bodies are little dewed, in tho 
comparison, the loose bodies, much. Now, as regards heat, tho 
loose bodies are very bad conductors ; they resist the passage 
of heat through them, and are therefore chosen as clothing. 

Let us now seek the interpretation of these three last re- 
sults of Concomitant Variations. The first and third relate to 
bad conduction of heat as a concomitant, the second to good 
surface- radiation. Now, both circumstances point to one re- 
sult, that is, surface cooling, in a cold atmosphere. A surface 
is cooled down by a cool contact, but if heat is rapidly sup- 
plied from within (which is good conduction) the lost heat is 
made good, and the fall of temperature is delayed, until the 
interior has cooled also. In bad conductors, the loss is not 
made good in the same way, and the surface temperature falls. 
Thus, bad conductors sooner become superficially cold, in a 
cold atmosphere. Next as to Radiation. The explanation 
here is still more easy. Good radiation is, by implication, sur- 
face cooling ; bad radiation, as from a polished metal surface, 
is retention of surface heat. We thus come round to the con- 
clusion, which a series of trials by the thermometer would 
have given at once, namely, that surfaces become dewed exactly 
as they fall in temperature. To all appearance, therefore, we 
have established a link of connexion between cooling and dew. 

The appearance is not the reality. There is still outstand- 
ing the fact that the same fall of surface temperature will not 
always bring out dew. Neither the same absolute surface 
temperature, nor the same difference between the surface 
temperature and the air temperature, is constantly followed 
by a deposit of moisture. We have here obviously a rcxulmd 
circumstance, whose investigation should next follow. The 
instances where the same thermometric diiference is unattended 
with dew need to be studied by exactly the same routine aa 



302 EXAMPLES OF THE EXPERIMENTAL METHODS. 

lias now been followed. We must look out for the suggestion 
of a possible agency ; and next subject that to experimental 
trial, with a view to proof or disproof. This residuum would 
a rise to a very arduous research if it had been left to 
experimental determination. The difficulty was conquered in 
another way. Already (1799) had Dalton published his theory 
aeons Vapour, or the Atmosphere of Steam, which was the 
missing link in the explanation of Dew. His positions were — 
that the aqueous vapour contained in the atmosphere is vari- 
able in amount, according to circumstances, and that the 
amount is limited by temperature. To each degree of temper- 
ature corresponds a certain amount, which is the saturation of 
the air at that temperature. An amount equal to one inch of 
mercury is sustained at 80°, half an inch, at 59°. Supposing 
the air saturated at any one moment, a fall of temperature 
will lead to precipitation as visible moisture ; but as the air is 
not always saturated, a fall of temperature will not bring 
dew or mist, unless the fall extends below the degree corres- 
ponding to saturation, called the temperature of the Dew- 
point. This is the residual circumstance, the thing wanted to 
complete the proof of the connexion of dew with surface cold- 
ness. 

The present instance is a case of Cause and Effect ; as may 
be shown in various ways. In the way that the case has been 
stated, there is not apparent any transfer of energy, which is 
the best criterion of causation ; but underneath the appearance, 
we find there is such a transfer. Heat is necessary to convert 
water into steam, and this conversion is an instance of the 
transmutation of power according to a definite rate of exchange. 
The withdrawal of the heat is followed by the re-collapse of 
the invisible vapour into water or visible moisture. So that 
the production of dew is clearly a sequence under the great 
law of transferred energy. Other proofs of causation are dis- 
pensed with by this decisive consideration. Mr. Mill, however, 
remarks, as a distinct criterion of cause and effect, as well as a 
means of settling which is cause, and which is effect, that cool- 
ing is a consequence of known and independent antecedents, 
and therefore cannot be set down as consequent on the occur- 
rence of dew. 

The next example is of value as showing the Experimental 
Methods in their purity, or in the absence of all deductive 
applications of laws, such as completed the enquiry into the 
cause of Dew. 



MUSCULAR IRRITABILITY AND PUTREFACTION. JUJ 

On the 16th of May, 1861, Dr. Brown-Sequard delivered the 
Croonian Lecture before the Royal Society, and took for bis 
subject the * Relations between Muscular Irritability, Cada- 
veric Rigidity, and Putrefaction.' In this he adduc< 
to maintain the following position : — 

' The greater the degree of muscular irritability at the time qf 
death, the later the cadaveric rigidity sets in and the longer ii 
lasts, and the later also putrefaction appears and the slower it 
progresses.' 

By muscular irritability is meant muscular power or apti- 
tude for contracting. A man fresh in the morning for his 
day's work would be said to have a good store of muscular 
irritability : at the end of the day's work, the stock is com- 
paratively exhausted. It would of course be still more ex- 
hausted after protracted fatigues continued through many 
days. 

The cadaveric rigidity is a stiffening of the muscles that 
occurs in all animals some time after death. The time when 
the stiffening begins, and the duration of it, are variable, and 
Dr. Brown Sequard tries to establish the law or cause or con- 
dition of this variation. This he does by a series of observa- 
tions, whose force will be appreciated by noting how far they 
comply with the exigencies of the experimental methods. 

First set of Experiments. — Paralyzed muscles. Here he has 
two connexions to establish, in order to the end in view. 
He first shows that the paralysis of a muscle leaves it for a 
time with more irritability than the unparalyzed or exerted 
muscles. He paralyzed the muscles of one leg in a dog, by 
section of the nerve. Five hours afterwards the dog is 
killed (by asphyxia). In the paralyzed muscles the irritability 
lasted ten hours ; that is, it was possible to induce contrac- 
tions in them (by stimulants) up to that time. In the healthy 
le^, the irritability lasted only four hours ; in other words 
was very much less. Now compare the results as regards 
Rigidity and the delay of Putrefaction — 

Duration of irrit. Duration of rigidity, commenced! 
Paralyzed M. 10 hours 13 days 17th day. 

Healthy „ 4 „ 5 „ 7th „ 

Here then is an experiment clearly of the nature of DiG'er- 
ence ; for two legs of the same animal were compared, and 
the only difference was the paralysis of one of them. It is 
true, as in all cases of vivisection, that an experiment of Dif- 
ference must always be received with caution, seeing that 

14 J 



3(>4 EXAMPLES OF THE EXPERIMENTAL METHODS. 

other changes may be made by the means taken to produce 
the difference. Yet, at all events, here is a strong presumption. 

The doctrine is confirmed farther by another aspect of the 
paralysis. If an animal is allowed to live a month after 
paralysis of a member, the paralyzed muscles are then inferior 
in irritability, and when compared under those circumstances, 
(bey become rigid and putrefy sooner. 

ad set of Experiments. — Effects of diminution of tem- 
perature upon muscles. — Dr. Brown-Sequard had determined, 
by previous experiments, that cold increases the vital proper- 
ties of the nerves and muscles — a fact on which the stimulating 
power of cold upon the animal system depends. He now 
applies this fact to the enquiry in hand. 

Two kittens of the same litter were placed in different tem- 
peratures. After death, the following differences were discern- 
ible. The one, kept at a temperature of 9S°.6, assumed the 
rigidity in 3^ hours ; this lasted three days, putrefaction 
commencing in the fourth. In the other, which had been kept 
so cool, that a thermometer inserted in the rectum stood at 
77°, the rigidity was delayed till the 10th hour, and lasted 
nine days, putrefaction commencing on the tenth. This experi- 
ment was repeated with many animals, and is also an experi- 
ment according to the Method of Difference. This is the 
general principle of the fact known in hot climates, that the 
dead putrefy almost immediately after death, and must be 
interred without a moment's delay. The relaxation of the 
vital powers in hot climates is only a part of the same fact. 
The full explanation of this point, or the resolution of the law 
into still higher laws is not yet fully made out. 

Influence of death by lightning and galvanism. — It was 
thought by John Hunter that animals killed by lightning did 
not stiffen. This has been found not the case. Still there are 
instances where the rigidity has either not set in, or been of 
so short duration, that its existence has not been traced. 
Lightning may kill in various ways :— 1st, By fright ; 2nd, By 
hemorrhage ; 3rd, By concussion of the brain. In all these 
three modes, there ought to be a manifestation of the rigidity. 
But there is a fourth mode, w T hich is to convulse all the 
muscles so violently as utterly to exhaust their irratibility ; in 
which case the rigidity may fail to be noticed. This is the 
way that galvinism acts upon animals. 

Experiments were accordingly tried by galvanizing the 
limbs of Rabbits; comparing the galvanized with the un- 
galvanized limbs, with respect to the time of rigidity. 



MUSCULAR IRRITABILITY AND PDTK1 

_ . _ . , G Limbt. 

Duration of Irn 

„ ( ofKigidity, - 

Putrefaction advance 
The experiments 

ninea-pigs were Bnbjected wholly to ga 
liferent degrees. In those powerfully 
Line, and thei\ 
ing rapid and brief. With a Less degree oi 
both phenomena was protracted. We have, 
additional corroboration of the law, still by I 
Lod of Difference. 

— This, of c< 
is a cause of diminished irritability. Now, there are \ 
ascertained facts that connect prolonged exertion with r 
putrefaction. Over-driven cattle and animals hunted to death 
putrify speedily. So in cocks killed after a fight. S 
killed in a very prolonged fight show the same phenomenon. 
The rigidity is quickly over, and the putrefaction rapid. 
These are instances of the Method of Agreement 

on muscles. — Dr. Brown- Sequard 
here collects confirming instances, from the comparison of 
cases where death happens in a well nourished condition of the 
musc.es, with cases where death had been preceded by inan I 
s, when men strong and fresh have been killed suddc 
the rigidity and pn -n have appeared very late. A 

is recorded of muscular irritability continuing twenty-six b 
in a decapitated man. Here is Agreement iu | 
Compare those instances with others of persons dying of - 
exhaustion, and the appearance is reversed. A man dying of 
prolonged typhoid fever, for example, was found to show no 
trace of rigidity, and putrefaction commenc :n an 

bour. This is Agreement in Absence. 

— It 
appears that muscles much attacked with cramps before 
speedily give way to putrefaction. 

Certain euniue) sometimes produce con- 

vulsions before death, and in those cases the rig.dity and 
putrefaction progress rapidly. 

a is an ample body of evidence from observation and 
experiment to establish the position .n. The Methods 

oi Agreement, of Difference, the Joint Meth I 

of Variations, have been all brought into \ 



306 FRUSTRATION OF THE EXPFJMENTAL METHODS. 

arc any doubts about the decisiveness of the experiments on 
the Method of Difference, from the possibility of making other 
changes besides the one intended, these doubts are. dispelled 
by the coincidence of results from so many distinct experi- 
ments. The research is purely Inductive. No consideration 
Deductive kind has been introduced; although there 
are general considerations that give great probability to the 
conclusion. Muscular irritability is the living condition 
of the muscle — its vitality — which may be greater or less; 
and the greater it is, the longer the muscle will retain its 
living characters, or the longer it will be in passing to the 
characters of death, which are rigidity and putrefaction. 
These, therefore, are delayed by fulness of vitality ; while loss 
of vitality hands the system over all the sooner to the 
destroyer. 

When we form conclusions, on an insufficient employment 
of the methods of elimination, w r e commit Fallacies of Induc- 
tion. Of these, numerous examples might be given, and the 
proper place for them is in the course of the exposition of the 
Methods themselves. As it is still the custom, however, to 
retain, in works of Logic, a separate chapter or book on 
Fallacies, we shall reserve for that part of the subject, the 
instances of Inductive fallacy. 



CHAPTER VIII. 
FRUSTRATION OF THE METHODS. 

1. In the Inductive Methods as hitherto contemplated, 
two conditions have been supposed ; first, that an effect 
has only one cause, or set of antecedents ; secondly, that 
different effects are kept apart and distinguishable. Both 
conditions may be wanting. 

In the method of Agreement, for example, it is assumed, that 
the effect a has only the cause A ; should A and C both be 
causes, the method would be defeated. The absence of A 
would not prove that it is not a cause; for the effect might 
still be due to C. The special difficulties attending this case 
must now be considered. 



PLURALITY OF CAUSES NOT FINAL. 

A rain, the effects ah c are supposed to stand out di 
may, ho or unit • 

the Intermix! 
is still more baffling to the inductive metho 
giv. 

PLURALITY OF CAUSB8, 

2. Ill many instances, the same effect :' 
Plurality of cacses : as Motion, Heat, I 

Bodies are put in motion by all the different agencL 
Prime Movers — animal strength, wind, 
tion (as in gunpowder), &c. Finding a body in 
therefore, we cannot ascribe it to any special agent, m 
from the fact that it is in motion : we see a wheel turning 
doing work, but we may not be able to attribute its :. 
one agent rather than another. In like manner, ther 
various sources of Heat ; the solar ray and combustion are 
the most familiar ; but friction a::d electricity are als 
Hence the fact of the evolution of heat does not point on 

3 ; as an example, uncertainty still attaches to the immedi- 
ate antecedent of animal heat. 

There are numeivus causes of pleasure and of pain : nume- 
rous modes of stimularing the nervov m ; numerous 
agencies of good health and of bad health ; numeiou 
getting a livelihood ; numerous causes of death. 

It is to be noted, however, that the plurality in some of 
these instances is on the surface only. As regards Motion 
law of the Persistence of Force assigns a common origin to all 
the so-called prime movers ; these, therefore, are , , and 

not the ultimate sources. The same law covers the produc- 
tion of Heat, however various the apparent antecedent-. The 
causes of Pleasure can be gene into a small number of 

agencies, if not into one. Possibly all stimulants may, in the 
be found to have a common effect on the sub- 
stance of the nerves. The ways to Wealth may be apparently 
many, but we can cover them all by one general 
earning and saving. In Health and E ::ii_:ht 

ibly be gene: 9 many pj 

cau - = I h. 

Lictical purposes, we have 

at the special embodiment of 
that cause, on a certain occasion. It is not en en a 

man is found dead, to assign the stoppage of the heart, or of 



308 FRUSTRATION OF THE EXPERIMENTAL METHODS. 

the lungs, or the extinction of the vital forces ; we desire to 
know in what form and circumstances these generalized causes 
were specialized ; whether by cold, by inanition, by poison, by 
mechanical violence, or otherwise. 

3. The chief consequence of Plurality of Causes is to 
frustrate the Methed of Agreement. 

The Method of Difference remains intact. Whatever be the 
plurality of causes of motion, if we observe the introduction of 
some one agent followed by the effect, we know the cause in 
that instance. There may be many ways of keeping up the 
animal heat, but the transition from the temperature of 60° to 
30°, by causing an immediate sense of chilliness shows that the 
external temperature is essential to comfortable warmth on 
that particular occasion. 

The operation of Plurality is to give uncertainty to the 
Method of Agreement. For example, we observe numerous 
cases of unhealthy human beings whose parents were un- 
healthy ; this would be to a certain extent a proof from 
Agreement. On the other hand, many unhealthy persons are 
the children of perfectly healthy parents ; whence, concluding 
by the strict rule of Agreement, we should affirm that 
unhealthiness in the parents is in no case a cause of unhealthi- 
ness in the children ; that the two facts are not in any way 
connected as cause and effect. The conclusion is obviously 
wrong ; it would be correct were there only one cause of ill 
health ; it is illegitimate if there be many causes. 

Plurality is illustrated by our English spelling. The 
method of Agreement is nullified in this instance. In certain 
words, the letters ough agree with a peculiar sound, as in 
* rough/ The same word occurs with other letters, as in 'ruff,' 
and the same letters occur with a different sound, as in 'bough.' 
Whence, by the Method of Agreement, we should infer that 
there was never any connexion between either sound and 
4 ough.' A similar illustration is afforded by ambiguous 
words. The word 'air' is spoken in company with a musical 
melody ; at other times it is spoken where there is no music; 
any one unprepared for plurality, and following out Agreement, 
would conclude that the connexion with music was purely 
casual'; that there was no fixed bond of union between the 
two. We acquire the meanings of the vocables of our language 
chiefly by the method of Agreement. We gradually eliminate 
all accompaniments that may be absent consistently with the 
employment of each word. We find, after a number of 

i 



FAILURE OF THE METHOD OF AGREEMENT 

repetitions of the word 'fire' in varions connexions, tbat tho 
one fact common to all is blazing combustion with heat W« 
learn in course of time to extend the word to metaphorical 
significations. These being conjunctions of pure 

without causation, they cannot be dealt with by any oth r 
method, while the occurrence of plurality, even when under* 

stood and allowed for, is a serious and painful distraction lo 
the inductive process. 

Again, pressure on the brain is a cause of insensibility; 
yet, as we find insensibility where there has been no pressure, 
we should say, according to Agreement, that pressure is not 
a cause. In the same way, every one of the causes might be 
proved not to be a cause — deficiency of blood, excess of dark 
unhealthy blood, rupture of the nervous continuity, &o. 

Extraordinary facts have come to light showing the possi- 
bility of exerting the mental powers, under disease of very 
large portions of the brain. These facts would seem to 
prove that such parts have no share in the mental functions. 
The safer inference is that there is a plurality of nervous scats 
or tracks for the same functions. It has long been supposed 
that the two hemispheres have common functions. 

The discussion of the problem of Beauty is often rendered 
fruitless by the neglect of Plurality. The attempt is made to 
assign some one circumstance present in all beautiful things — 
as Colour, Harmony, Fitness, Unity, Suggestion of Mental 
qualities. Now, by the unqualified method of Agreement, 
every assignable circumstance could be dispi oved ; with refer- 
ence to each one in turn, would it be possible to find objects 
of unquestioned beauty where that one is not present. Jeffrey 
thinks it a sufficient refutation of the theories he opposes, 
to produce beautiful objects where the alleged source of beauty 
is absent. 

4. The counteractives to the failure of Agreement, in 
the case of Plurality, are (1) great multiplication of in- 
stances, and (2) Agreement in absence, that is, the Joint 
Method. 

(1) One remedy for the failure of the Method of Agreement, 
under Plurality, is multiplication of instances. This will 
operate in various ways. It will tend to bring out all the 
causes; which is one desirable issue of Plurality. An ex- 
tended statistics of Crime or Pauperism will show us the pos- 
sible agencies, by giving a wide scope for elimination. The 
long experience of medical practitioners has taught them 

1 



310 FRUSTRATION OF EXPERIMENTAL METHODS 

nearly all the possible causes of the greater number of 
diseases. At this stage of exhausted plurality, the only point 
for enquiry, in the special instance, is — Which of the causes 
are present, and are these free to operate ? Knowing, all the 
contributing causes of Pauperism, we ask which of these occur 
in England, in Ireland, or in Scotland, and are they free or 
uncounteracted ? Being aware of the various antecedents of 
dyspepsia — bad food, too much food, too little food, hard labour, 
want of exercise, intemperance, mental wear and tear, bad air, 
a hot climate, &c. — we can judge what brought on the disease 
in a given instance. 

It' we do not know which causes are present on a given 
occasion, and whether those actually present are counteracted, 
mere Agreement is wholly fallacious. The fallacy named post 
hoc, ergo propter hoc, is an abuse of Agreement, where elimina- 
tion is vitiated by Plurality, as in a great number of political 
inferences. It is remarked that Protestantism is accompanied 
with superior industry ; the instances attainable are insuffi- 
cient in number to eliminate other causes. 

(2) The other remedy is the Joint Method. We should seek 
out cases of Agreement in absence, which are of a very decisive 
nature. If in all cases where a particular effect fails, one par- 
ticular cause is absent, there is, in spite of possible plurality, 
a strong presumption that the two circumstances are cause 
and effect in those instances. The reason grows out of that 
close approach to the Method of Difference furnished by 
Agreement in absence. Although there are various causes of 
]jghfc> jet the union of agreement in presence with agreement 
in absence is sufficiently decisive of the connexion of light 
with a high temperature. The special connexions of light 
with low temperature are not denied ; they are admitted as 
exceptions to agreement in absence, as a residuum to be ac- 
counted for. We know one cause thoroughly ; we find there 
are other causes, as yet imperfectly known, which have this 
uncertainty, namely, that a body at the common temperature 
of the air may possibly be luminous. 

THE INTERMIXTURE OF EFFECTS. 

5. The Methods of Elimination suppose different effects 
to remain separate and distinguishable ; whereas cases 
arise where the effects of different causes unite in a homo- 
geneous total. 

When, in an aggregate phenomenon, distinguishable ante- 



INTERMIXTURE OF 1 ; ;;Il 

cedents produce distinguishable consequents— A 
a b c, and A D E giving a d e, the experimental metb 
operate to advantage. The combination of wind, rain b 
increased temperature, produces a combination of distinen 
able effects— waves on the surface of water, Booding of streo 
the sensation of warmth. 

In other cases, and these very numerous, the effect of tho 
several causes is homogeneous, and is merely incre 
amount by the concurrence. The sea is fed by innnmera 
rivulets. The wind often concurs with tidal ag 
to produce a higher tide. A body propelled b 
movers, as when a train is urged by three locomotive engines, 
shows only one effect, velocity of movement. The moon's 
path is a resultant of the attractive forces of the sun and 
the earth combined with its projectile movement. The path 
of a comet is the resultant of many influences; it does not 
bear on the face of it the story of them all. An invalid repairs 
to some salubrious spot, and plies all the means of restoration 
to health ; many influences combine to the result, but the 
effect is one and indivisible. 

A still more perplexing situation is the conflict of opposing 
agencies. In an equal balance nothing is seen, and yet great 
powers have been at work. In unequal contests there is an 
effect ; but that effect does not suggest the fact of conflict. A 
trader has a net profit at the end of the year ; the statement 
of that profit, however, gives no information of his expenditure 
and receipts. The patient may be under various healthy 
stimulants, each working its proper effect ; but some one 
noxious agency may counteract the whole. 

Natural agencies can never be suspended ; they may be 
counteracted by opposite agents. The force of gravity is not 
interfered with when a balloon rises, it is merely opposed by a 
greater force ; it still operates but in a different form. Inst' 
of causing the usual appearance, namely, the descent of bou 
to the ground, it operates to diminish the effect of an upward 
force, the buoyancy of the air (itself an indirect c ce 

of gravity). 

A counteracted force is technically said to exist in tend 
There is a tendency in all bodies to descend to the ground ; in 
water to find its level ; in the moon to move towards the earth, 
and towards the sun. There is a tendency in human beings to 
seek their own interest; in despotic sovereigns to abuse their 
power. The tendencies are not annihilated when they fail to be 
realized; they are onlycounteractedbvsome opposing tendencies. 



312 FRUSTRATION OF THE EXPERIMENTAL METHODS. 

A farther circumstance working to invalidate the operation 
of the methods is the mutuality of cause and effect In political 
causation, this is illustrated by Sir G. C. Lewis as follows :— 
4 It happens sometimes that when a relation of causation is 
established between two facts, it is hard to decide which, in 
the given case, is the cause and which the effect, because they 
net and re -act upon each other, each phenomenon being in 
tarn cause and effect. Thus, habits of industry may produce 
wealth ; while the acquisition of wealth may promote industry : 
again, habits of study may sharpen the understanding, and 
the increased acute n ess of the understanding may afterwards 
increase the appetite for study. So an excess of population 
may, by impoverishing the labouring classes, be the cause of 
their living in bad dwellings ; and, again, bad dwellings, by 
deteriorating the moral habits of the poor, may stimulate 
population; The general intelligence and good sense of a 
people may promote its good government, and the goodness of 
the government may, in its turn, increase the intelligence of 
the people, and contribute to the formation of sound opinions 
among them. Drunkenness is in general the consequence of 
a low degree of intelligence, as may be observed both among 
savages and in civilized countries. But, in return, a habit of 
drunkenness prevents the cultivation of the intellect, and 
strengthens the cause out of which it grows. As Plato 
remarks, education improves nature, and nature facilitates 
education. National character, again, is both effect and 
cause ; it re-acts on the circumstances from which it arises. 
The national peculiarities of a people, its race, physical struc- 
ture, climate, territory, &c, form originally a certain character, 
which tends to create' certain institutions, political and domes- 
tic, in harmony with that character. These institutions 
strengthen, perpetuate, and reproduce the character out of 
which they grew, aud so on in succession, each new effect 
becoming, in its turn, a new cause. Thus, a brave, energetic, 
restless nation, exposed to attack from neighbours, organizes 
military institutions ; these institutions promote and maintain 
a warlike spirit ; this warlike spirit, again, assists the develop- 
ment of the military organization, and it is further promoted 
by territorial conquests and success in war, which may be its 
result— each successive effect thus adding to the cause out of 
which it sprung.' (Methods of Politics, I. p.' 375). 

6. The Intermixture of Effects is a bar to the Experi- 
mental Methods. 



INTERMIXTURE OF EFFEl J1J 

If A B C D conspire to yield, not aba d, but a; and if 
A B C F yield still a, nothing is eliminated, there is no pro- 
gress. If a were precisely measurable, and if its variation* 
corresponded definitely to the removal of particular agents, 
the Method of Difference would cope with the case? the 
omission of A followed by the reduction of a to J a, would be 
a proof that A produced \ a. But the Method of Agreement, 
in its proper character of varying the circumstan© 
eluding some agents and including others, could not furnish 
a decisive proof, so long as a represented the sum of several 
effects. 

Now, as in many departments, effects are thus inextricably 
blended, we should be at a stand-still, were we not in po 
sion of some method more searching than Agreement. Even 
in the Inorganic Sciences, as Mechanics and Chemistry, wo 
have this complication ; in Biology, Mind, and Society, we 
have it still more. A good crop is a single effect ; the agency 
may be multifarious. A voluntary action may be the result- 
ant of several motives. The rise and fall of prices, the general 
prosperity of a country, the increase of population, seldom 
depend on one cause exclusively ; yet the effect in each case 
is, to our eyes, homogeneous. 

Concomitant Variations is the only one of the Methods that 
can operate to advantage in such cases. If a cause happens 
to vary alone, the effect will also vary alone, and cause and 
effect may be thus singled out under the greatest complica- 
tions. Thus, when the appetite for food increases with the 
cold, we have a strong evidence of connexion between those 
two facts, although, other circumstances may operate in the 
same direction. 

The assigning of the respective parts of the sun and moon, 
in the action of the Tides, may be effected, to a certain degree 
of exactness, by the variation of the amount according to the 
positions of the two attracting bodies. 

By a series of experiments of Concomitant Variations, directed 
to ascertain the elimination of nitrogen in the human body 
under varieties of muscular exercise, Dr. Parkes obtained the 
remarkable conclusion, that a muscle grows during exercise, 
and loses bulk during the subsequent rest. 

For the first of the difficulties now illustrated — Plurality, 
with the aggravation of counteracting influences — an import- 
ant instrument remains, an additional Method of Elimination, 
termed ' Elimination by the Computation of Chance.' For 



CHAPTER IX. 
CHANCE, AND ITS ELIMINATION. 

1. An important resource in eliminating the irrelevant 
antecedents or accompaniments of an effect is obtained 
through the calculation of Chance or Probability. 

This is to approach the problem of Induction from a novel 
aspect. Instead of varying the circumstances so as to procure 
the absence of the several antecedents A B C in turn, we 
consider whether these agents might not be present of them- 
selves without any regard to the effect in question. Thus, a 
person dies at midnight, when the sun is below the horizon 
and due north. Now, seeing that this event happens every 
twenty-four hours, as a consequence of cosmical operations, it 
must come round and must coincide with a great many 
things that happen on the earth. The fact of such coincidence 
is not of itself held as proving causation or regular concomi- 
tance with everything that happens at that time. Before we 
presume a concurrence of causation between two coinciding 
tilings, we enquire whether the two things are not equally 
liable to concur, whether connected or unconnected. 

The night that Oliver Cromwell died, a great storm devas- 
tated London. The coincidence might affect the minds of the 
superstitious, but there was no proof of causal connexion. 
Each event grew out of its own independent series of causes 
and conditions ; the one was a consequence of the bodily con- 
stitution and manner of life of Cromwell ; the other "was a 
consequence of the laws of the atmosphere. They concurred 
in time, and that is all that should be said regarding them. 

Every event of every man's life must concur with some one 
position of the planets, on the supposition of their being no 
connexion whatever. Hence, such concurrences prove nothing 
at all ; they are left out of account without even the trouble of 
elimination. 



314 CHANCE, AND ITS ELIMINATION. 

dealing with the same uncertainty, and for the still greater 
(and often accompanying) uncertainty of Intermixture of 
Effects, the chief resort is to Deduction. The two next chap- 
ters will be occupied with those two subjects. 



MEANING OF A CHANCE COINCIDENCE. 

There are cortain cases, where a oause fails to produ 

effect, being counteracted by some other i 
followed by b c cl, from which the inferenoe, I merit 

would be, that A is not the cause of a. Bark is administered 
to a patient in ague, but the symptoms are not alleviate-. I. The 
strict application of the Method of Agreement would lead to 
the inference that bark does not euro ague. Vet wo <l<> not 
in practice, lose faith in medicines from individual failures. 
We are prepared to encounter exceptions to ca* impli- 

cated causation. The question then comes, how far is tins to 
go ? How are we to be sure of causes at all, if they fail to 
torork their effects? What difference can we draw between 
such instances and mere accidental concurrences ? 
^ The theory of Chances, or Probabilities, applies to both the 
situations now illustrated ; — the dropping without the trouble 
of elimination what would be present whether another thing 
were present or not ; and the proving of a causal agent, 
although not uniform in producing the proper effeet. 

2. A chance coincidence is one where thore is no implied 
connexion of cause and effect, or one that would be the 
same in the absence of any such connexion. 

Instances have been already given, and could be multiplied 
at pleasure. A person walking on the sea shore at a certain 
hour every clay, will, on a given day, walk at low water ; but 
the concurrence is said to be a chance concurrence, as the 
person's walking is not in any way regulated by the state of 
the tide. On the other hand, the concurrence with the time 
of day is not chance. There is a concurrence in botli cases ; 
the one without cause, or a matter of chance, the other with 
a cause, and not a matter of chance. 

If it is proposed to enquire what coincidences are due to 
chance and what not, the method is dictated by the so-called 
rules of Chance. 

Common sense suggests the principle of the solution. We 
know that low tide coincides with a certain hour of the day 
twice a month. If, on a long average, the coincidences of low 
tide and the person's walking on the shore happened exactly 
twice a month, we should say the relationship is casual, 
accidental, or without any link of causation; for on the supposi- 
tion of there being no connexion, this number of coincide 
might occur through the laws of tides. If, on the other hand, 
the two facts coincided daily, we should presume a coincidence. 
Moreover, even if it did not occur daily, but once or twiee a 



316 CHANCE, AND ITS ELIMINATION. 

week, this would be more than chance would account for, and 
there would be a presumption of a causal connexion, which, 
however, is liable to be defeated or counteracted. 

So with the connexion between the walking and the hour 
of the day. Suppose the person might walk at any time dur- 
ing fifteen hours of the day, he would, by mere chance, walk 
during any particular hour, once every fifteen days on a long 
average, if in fact, some one hour coincided with the walking 
only once in sixty days, there would be proof of an influence 
hostile to going out at that hour; if at some other hour, the 
walking occurred six days in seven, there would be proof of 
positive connexion with the said hour. 

These obvious considerations are reduced to principles and 
rules in the logico-mathematical science called the ' Doctrine 
of Chances or Probabilities. ' 

3. The principle is as follows : — Consider the positive 
frequency of the phenomena themselves, and how great 
frequency of coincidence must follow from that, supposing 
'there is neither connexion nor repugnance. If there be a 
greater frequency, there is connexion ; if a less ; repugnance. 

This may be called the general case, as distinguished from 
certain modified cases to be stated afterwards. 

If we find from observation (sufficiently extended to genera- 
lize the facts) that A exists in one instance out of every two, 
and that B exists in one instance out of every three ; then, if 
A and B are wholly indifferent to each other — neither con- 
nected nor repugnant — the instances of A and B happening 
together will be (in the Arithmetic of Chances) one out of 
every six, on a sufficient average. If, really, the two co-exist 
oftener, there is connexion ; if seldomer, repugnance. 

By this method singly, could we determine a connexion of 
cause and effect in the instance of rain occurring with a par- 
ticular wind, say the South- West. The experimental methods 
fail in such an instance. It is well remarked by Mr. Venn 
(Logic of Chance, p. 127) 'that in Probability we distinctly 
take notice of, and regard as evidence, reasons so faint that 
they would scarcely be called by any other name than mere 
hypothesis elsewhere.' 

In the Chinese astronomical observations, frequent entry 
was made of new stars ; and by far the larger number of these 
appeared in the milky way. The coincidences implied some 
law of connexion, but no such law was suspected by the 



I 



PROOF OF LAWS NOT UNIFORM} jflf 



Chinese astronomers. We now know that the milky w.iy 
contains the great mass of the stars of our gala.w 
quently all changes connected with the stars will be 
numerous there. The circumstance has been adverted I 
an important confirmation of the accuracy of the Chi 
astronomical records. 

In the generalizations of co-inhering attributes, in Phj 
and in Chemistry, there is often a want of perfect agreeo 
in the details: yet the agreement is too extensive to he the 
product of chance, and hence we must admit the ezistenc 
a law, which, in the complications of the phenomena, is i 
sionally crossed and counteracted. It is a law that the alka- 
Hue bases are oxides of the metals ; a remarkable exception 
occurs in ammonia. The law does not become waste paper 
because of this exception. The coincidence is one that mere 
chance cannot account for ; and some way has to be sought 
out to reconcile the discrepancy. Perhaps an expression will 
be found that will apply alike to ammonia and to the other 
alkalies. The discovery of a metal in ammonia has been 
looked to as a solution of the difficulty. 

Many genera of plants are centralized in definite geogra- 
phical areas, Erica, for example ; the species being coiiected 
within a certain tract, at some one point of which there is 
found the maximum number of species. As chance cannot 
account for such localizations, the endeavour is made to trace 
out laws of connection (cause and effect) between the plants 
and the locality. 

In the controversies raised on the subject of Phrenology, 
the opponents of the system have considered that they dis- 
proved it by instancing decided exceptions to the phrenological 
allocation of faculties — cases of mathematicians with a small 
organ of number, or musicians with a small organ of tune. 
The facts supposed, however, are not conclusive against the 
system. For, in the first place, the disproof of the coincidences 
alleged, in respect of one or two faculties, or any number, 
would not disprove all the rest. But, in the second place, a 
few exceptions would not thoroughly disprove the alleged 
connexion ; they would only disprove its unfailing uniformity. 
The phrenologist could still retreat upon the principle we 
are now discussing; for, if the coincidences of a certain 
distinguished mental aptitude, — as number, music, colour — - 
with the unusual size of a certain region of the head, were 
more frequent than it would be on mere chance, or in the 
absenc3 of all connexion, he would be entitled to infer a 



31S CHANCE, AND ITS ELIMINATION. 

relationship between the two. No doubt, the practical value 
of the tacts would be very much lowered by the supposed 
relationship being frequently defeated ; still, the bond must be 
considered as established. In this view, an extensive series of 
observations on tbe size and form of the human head, and on 
the accompanying mental qualities, if reduced to a statistics 
of comparative frequency, could yield indications of the loca- 
lizing of mental functions, if such be the actual case. 

The homoeopathic maxim 'similia similibus curantur,' may 
De subjected to the same criticism. Exceptions do not nullify 
the principle, although they reduce its value as a guide. Both 
this and the opposite maxim ('contraria contrariis curantur') 
may hold in nature. The coincidences in both cases may be 
greater than chance would account for. 

The prevalence of the different forms of Christianity after 
the Information shows a coincidence with Race that chance 
would not account for. The Greek church was propagated 
principally in the Slavonic race ; the Roman Catholic church 
coincides largely with the Celtic race ; and the Protestant 
church has found very little footing out of the Teutonic races. 
From this coincidence must be presumed a positive affinity 
between the several forms and the mental peculiarities of the 
races : — which, as an empirical law, may be applied to cases 
immediately adjacent, and as a derivative law (so it may be 
considered; may be applied still wider. We may fairly con- 
clude, that any speedy conversion of one church to another is 
very unlikely. But the law being at best a derivative law, 
involving a plurality of simpler uniformities under collocations 
or co-efficients, may be subverted by circumstances arising in 
the lapse of time. It might also happen that change of place 
and of circumstances might defeat the law ; such as emigra- 
tion to other countries, or great political revolutions. 

We may apply the principle to the problem of the Spread of 
Language. The articulate modes of the human voice being 
nearly the same in all races, there would be a great many 
common words struck out, without any communication be- 
tween the races. Then it might happen too that some of 
these common words might be applied to the same objects, 
because some name or other must be applied. Of course, the 
probability of the same sound as the radical ma, being ap- 
plied to the maternal parent, by different races independently 
is a very small probability; and the probability of any great 
number of such coincidences is still smaller, therefore, tf we 
Bnd m the languages of India, and of Great Britain, a very 



COMBINATION OF CHANCE AND I 

considerable number of names almost the very 
to the same things, we must conclude that 
not the work of chance, and is the result of 

4. A special case of the elimination of chance 

sented by the combination of Chance with or of 

casual and causal links. In a sufficiently proli 
perienee, chance may be eliminated. 

Thus, so far as the mere decay of the human system is con- 
cerned, deaths would be equally frequent at all periods of the 
year, and at all hours of the day. In the statistics of Morti 
however, we find that some months are marked by an e 
live number of deaths ; as December, January, and February. 
This points to a law of connexion between winter severi! . 
mortality. In the same way, if we had the statistics of the 
deaths occurring at different hours of the day. we might find 
a greater number occurring in the depressing hours of the 
night, namely, between midnight and dawn. There is au 
element of chance, and an element of law ; the chance can be 
eliminated by statistics, and the law ascertained and estimated. 
The combination of chance and law is seen in the progress of 
the seasons. The Chance element is the fluctuation from d:iy 
to day, due to meteorological changes, which, in our ignorance, 
we view as fortuitous. The Law is the progress of the sun, 
which if undisturbed would be shown in the steady increase of 
temperature from January to' July, and reversely. The influ- 
ence of the winds interferes with this regular course ; but by 
averages taken for many years, we could ascertain for any one 
place the temperature proper to each day of the year, through 
the solar influence alone. 

The skill of a player at cards is shown by his winnings at a 
year's end. So, the keeper of a gaming table, in spite of daily 
fluctuations, has a sure profit in the long run ; the table being 
constructed with a definite percentage in his favour. 

In taking observations, it is usual to multiply instances, and 
to strike an average. This eliminates mistakes of th e 
accidents, and ail errors that do not grow out of some perma- 
nent bias. 

5. A third form of the elimination of chance is the 
discovery of causes so small in amount as to be submerged 

by the casual accompaniments. 

Loaded dice are detected after a long series of throws. 
Actual trials have shown that, in the course of 1200 throws, 



829 CHANCE, AND ITS ELIMINATION. 

there would be very nearly 200 turns-up of each side. Any 
great deviation from equality would be a proof of loading. 

It was by the average of many daily observations of the 
barometer that the diurnal variations were discovered. Those 
periodical variations were too small to be noticed in the midst 
of the fluctuations from day to day; but the elimination 
of these last by a long course of observations brought the other 
to light, and gave their amount. 

A small bias in an instrument might be detected by great 
multiplication of instances. All the chance errors would be 
eliminated, and would show a residuum, to be accounted for 
only by some permanent bias. 

PRINCIPLES OF CHANCE OK PROBABILITY. 

6. Probability expresses a state of the mind, and also a 
situation among objective facts. 

As a state of the mind, it is a grade or variety of Belief. 
The highest degree of belief is called Certainty ; the inferior 
degrees are degrees of Probability. The psychological criterion 
of strength of -belief is readiness to act. 

As a situation of objective facts, it points to our experience 
of the recurrence of events with more or less uniformity. 
What happens always, under certain circumstances, — as the 
rise of the sun, the termination of human life — is called cer- 
tain ; our assurance in such instances is at the highest. What 
happens, not always, but sometimes, — as that the sun rises in 
a cloudless sky, that men live seventy years— is not certain. 
Neither the fact, nor the failure of the fact, is certain. To 
this middle situation, is applied the term Probability. 

At a first glance, we might be disposed to say that such 
events are positively uncertain ; that any judgment as to their 
happening is incompetent ; that we are in as great ignorance 
as to whether the sun will ever rise clear, or whether any man 
will live to seventy, as if we had never known the sun to rise 
or any man to die. Tn this emergency, however, we derive 
an aid from extended observation. If, in the same locality, 
we observe the rise of the sun for a great many days, we find 
that the rise in a clear sky happens in a certain fixed propor- 
tion, which is more and more steady as observation is pro- 
longed. So, if we keep a record of the duration of men's 
lives, ^ for a considerable period of time, we find the seventy 
years' lives to recur in a fixed proportion, the more steady the 
longer the records are extended. Hence, if it is of any value 



I 



PRINCIPLES OF CHANCE. 



to us to know how many days in the year the sun rises rloti.l- 
less in a given climate, or how many men live to B6\ 
can obtain the information with absolute certainly. 

Now, there are many occasions when this know 
proportionate recurrences of events, or of what i 
averages, is of the highest practical moment. It is m 
to cite, among other examples, the system of Insurance, which 
is wholly built upon it. 

7. When a sufficiently extended series of observations 
shows a fixed proportion in the relative ocounenc 
events, this proportion is called the Probability of the 
occurrence of any single event ; which, however, is a fiction; 
meaning only the certainty of the proportion, or average, 
on the whole. 

If, in the run of many years, it appears that there have been, 
in some one place four dry days for three wet, then it is a. 
matter of inductive certainty, that in the future that propor- 
tion will hold. TVe may stake any practical interest upon the 
recurrence of that proportion. But we are unable to say, be- 
fore hand, of any one day whether it will be wet or dry. Still, 
a convenient fiction is used applicable to a single day. We 
see that the chances or probabilities are that some given day 
will be dry. A numerical expression is used for the degree of 
the probability ; it is said to be four to three in favour of dry- 
ness, or against rain. This does not mean that we gajn any- 
thing in a single case ; a case taken apart must be held as 
absolutely uncertain. Unless we act upon the gross or total, 
we gain nothing by taking into account the numerical pro- 
babilities with a view to a single instance. 

Bat although we are no ^iser as to the individual day that 
we desire to be dry or wet, yet, as there are a great many 
similar emergencies in life, where we have to apply aver 
to single cases, — by following the measure of probability on all 
such occasions, and on all subjects, we shall be oftener right 
on the whole, than if we were to neglect this probability. 
This is the justification of our presuming that a given day will 
be dry and not wet, under the probability assigned. 

8. It is found that the experienced recurrence of events 
coincides with an estimate formed thus : — Suppose that we 
know of several events that some one will certainly happen; 
and that nothing in the constitution of things determines 
one rather than another ; in that case each will recur, in 



322 CHANCE, AND ITS ELIMINATION. 

the long run, with a frequency in the proportion of one to 
the whole* 

Tims, in the familiar case of tossing a penny, there is sup- 
po3ed to bo nothing in the form of the coin, or in the impulse 
given to it, to determine one side rather than another. In 
this case, every second throw will, in the long run, be luads. 

So, in throwing dice, if they are fair, every sixth throw, on 
a long series of trials, will give ace. 

An a priori necessity has been assumed for this proportionate 
recurrence of events. Such a necessity appears to be justified 
in the tossing of a penny ; we seem to be in a state of equipoise 
between the two possibilities of head and tail, and feel that 
any inequality in the result would be without reason or cause. 
Accordingly, we are apt to assume, as a necessity of the case, 
that the turning up of head and of tail should be equally 
balanced at the end of a long trial. The fact is, however, that, 
in this and like cases, we are exceptionally circumstanced in 
point of knowledge ; we know what are the causes at work, 
and that there is nothing to give a bias in the long run to 
either side of the penny. 

In the more complicated cases, as human life, shipwrecks, 
fires, &c, we should not be disposed to predict anything before 
hand from such considerations as the above. We should not 
consider all years, from one to ninety, as equally open for men 
to die in, or that the year of age is quite indifferent. We soon 
come to know better ; and, refraining from a priori supposi- 
positions we trust solely to induction from a sufficiently 
prolonged basis of actual observation. ' 

9. The important theorems growing out of the general 
principles and applied to problems in Logic, are these. 

I. The probability of the concurrence of two indepen- 
dent events is the product of the separate probabilities. 

If A occur once in six times, its probability is £, or one for 
and^five against; if B occur once in ten times, its probability 
is y 1 ^, or one for, and nine against ; the probability,. or relative 
frequency i n the long run, of the concurrence of the two is 
eV~~ one f° r an d fifty-nine against. 

This rule is an arithmetical consequence of the general for- 
mula, and does not need a separate appeal to observation and 
induction. Suppose two days in three are dry, and one in 
three nas a westerly wind, then (if the two phenomena were 



COMBINATION OF PROBABTUTlta 

independent), the chance is if X X or 2 . t } Klfc is tw() (of 
Be von against. 

10. II. The probability of the occurrence of on 
of two events that caun L ris the sum of tl 

probabilities. 

'If one man in ten is over six feet, and one in ; 
five ; then in a large number, say 120,00 ', there will be ab 
12,000 over-six-feet men, and about 10,000 nnder-fire-i 
men ; the sum of the two 22,000, will represent tb 
such as are one kind or the other.' 

11. III. The rule for the cumulation of independent 
Testimonies in favour of a fact, is to multiply the numl 
expressing the proportionate value of each Testimony. 

If a witness is correct six times out of seven, or speaks six 
truths for one error, his relative testimony is six for and one 
against, or f. Two witnesses of this character concurring 
would give a probability of 6 to 1 multiplied by G to 1, or 
06 to 1, and so on. 

12. IV. The rule for the deterioration of testimony in 
passing from one person to another, that is, for the weaken- 
ing of traditional evidence through lapse of time, is to 
multiply the fractions expressing the separate probabilities. 

If one witness speaks truth five times in six, the fraction is 
% ; if another witness speaks truth nine times in ten, the value 
is T 9 ^j. If the one repeats what he has heard from the other, 
the testimony is weakened by the transmission to £ < 
= -£|, or |. Of facts attested by the second witness, de- 
riving from the first, three will be true and one false. A few 
such transitions bring the evidence below probability, and 
render it worthless. Four successive witnesses each valued 
f , would give o^V' w bich would be a probability against their 
testimony. Xow, there are many cases where a testimony is not 
put too low by the above fraction ; if a want of perfect veracity 
is joined with inadequate comprehension of the etateme 
weak memory, or other infirmity, a witness would not be cor: 
three times in four. 

The application of the Theory of Probabilities to the induc- 
tive determination of Causes is given in the following theorem 
taken by Mill from Laplace. 



824 CHANCE, AND ITS ELIMINATION. 

13. * Given an effect to be accounted for, and there being 
several causes that might have produced it, but of whose 
sence in the particular case nothing is known ; the 
probability that the effect was produced by any of these 
causes is as the antecedent probability of the cause, multiplied 
hi/ the probability that the cause, if it existed, would have pro- 
duced the given effect. J 

'Let M be the effect, and A, B, two causes, by either of 
which the effect might have been produced. To find the pro- 
bability that it was produced by the one and not by the other, 
ascertain which of the two is most likely to have existed, and 
which of them, if it did exist, was most likely to produce the 
effect M ; the probability sought is a compound of these two 
probabilities. 

' Case I. Let the causes A and B be both alike in the second 
respect : either A or B, when existing, being supposed equally 
likely (or equally certain) to produce M ; but let A be itself 
twice as likely as B to exist, that is twice as frequent a pheno- 
menon. Then it is twice as likely to have existed in this case, 
and to have been the producing cause of M. 

' Case II, Reversing the last supposition, let us suppose that 
the causes are equally frequent, equally likely to have existed, 
but not equally likely, if they did exist, to produce M ; that in 
three times that A occurs, it produces that effect twice,. while 
B, in every three times produces it but once. Since the two 
causes are equally frequent in their occurrence, in every six 
times that either exists, A is three times and B three times. 
But A in three occurrences produces M in two ; while B in 
three occurrences produces M in one. Thus, in the whole six 
times, M is produced thrice, but twice by A and once by B. 
So that the probability is in favour of A in the proportion of 
two to one. 

' Case III. Let there be an inequality in both respects. Let 
A be twice as frequent as B ; and let A produce the effect 
twice in four times ; B thrice in four times. Then the 
antecedent probability of A to B is 2 to 1 : the probability 
of their producing M is as 2 to 3 ; the product is 4 to 3. 
In other words the probabilities in favour of A being the 
cause are as 4 to 3. And so on with any other combination.' 
^ The principle may be applied to distinguish casual coin- 
cidences from those that result from law. ' The given fact 
may have originated either in a casual conjunction of causes, 
or in a law of nature. The probabilities, therefore, that the 






CHANCE AITLIKD TO CAlSATION. 

fact originated in these two modes, are us their anteo 

probability multiplied by the probabilities that if tb 
they would produce the effect. Hut the peculiar con 
ot chances, it it occurred, or the law of nature if real, would 
certainly produce the series of coincidences.' The probabilities 
therefore, are as the antecedent probabilities of the causes' 
One of these-the antecedent probability of the combination of 
mere chances that would produce the given result— is an 
appreciable quantity, on the principles already laid down 
The antecedent probability of the other may be estimated mure 
or less exactly, according to the nature of the case.' 



CHAPTER X. 
INDUCTION AIDED BY DEDUCTION". 

L It is desirable at every stage to carry out Inductive 
laws into their Deductive applications. Now, Deductions 
cannot be made or verified without Observation of facts. 

. Deduction or Ratiocination, in its purely formal aspect, is 
given in the Syllogism. In its material side, it involves the 
comparison of facts, and is akin to Induction. We have yet 
to view it as it plays a part in the Inductive Sciences. 

2. The full scope of the Deductive Method comprises 
three operations. 

I. There must be certain pre-established Inductions. 

We must somehow arrive at Inductive Generalizations, and 
next prove them when arrived at. The Experimental Methods 
have in view these two ends, and especially the last, namely, 
Proof. Incidentally, the methods indicate the mode of Dis- 
covery, but they have not been expressly aimed with that view. 
It has been apparent, however, that the collection and study of 
instances, under the Method of Agreement, must suggest tho 
points of Agreement, when we are ignorant of them, which is 
to suggest a general law. Our examination of the problem of 
Crystallization, and the enquiry into the cause of Dew, led 
first to the discovery, and next to the proof, of generalized 
coincidences. Still, it was not advisable to carry on a double 



326 INDUCTION AIDED BY DEDUCTION. 

illustration, by moans of the Experimental Methods, to eluci- 
date at once Discovery and Proof; of the two ends, the 
kxrician has most to do with the second; Proof is his main 
object, for which he can lay clown definite laws ; Discovery is 

valuable end, likewise, but it is not equally amenable to 
prescribed rules. 

[n the management of particular instances, with a view to 
the Discovery of generalities, assistance may be obtained in the 
three following ways : — 

(1) The number of instances should be as extensive as pos- 
sible. In the comparison of a large number the mind will be 
struck with points of community, from the very fact of the 
recurrence ; as in the examples collected in the research on 
Dew. Moreover, there will start forth some one that contains 
the circumstance sought, in startling prominence ; these* are 
the glaring or suggestive instances. Such, in the case of 
Dew, was the example of the warm breath upon a cold iron 
surface, as a knife blade. 

(2) When out of mere number and variety of instances, ihe 
identity does not .flash upon the mind, the next thing is to 
select a few for careful scrutiny. Each instance should be 
studied in isolation, should be gone over in every minute point, 
and examined from every side ; the features being exhaustively 
set down in writing. After a few separate instances have been 
considered in this thorough way, the resemblances (unless at 
the time inscrutable for want of other lights) will become 
apparent to the view. Newton's study of the phenomenon of 
the coloured rings of the soap-bubble, was an exercise of the 
severe mental concentration now described. 

(o) The general laws of phenomena must be sought in the 
cases where they are least complicated or combined with other 
laws. This is an obvious precaution conducing to Discovery. 
The laws of motion are studied in simple cases, such as straight- 
lined movements, or wheel-movements, under a single impulse. 
Gravity is lest studied in bodies falling perpendicularly, where 
there is no other force operating. Neither the first law of motion, 
nor the law of gravity, could have been advantageously genera- 
lized, in the flow of rivers, or in the motions of the planets. 
1 hese complications are not suited for inductive discovery, but 
for deductive application, as at present contemplated. The 
hrst principles of Optics are sought, not in the workings of the 
eye, nor in complicated lenses," but in the simple mirror fcr 
reflexion, and in the plane transparent surface for refraction. 
ko the more transce. dental powers of light, in cat sing mole. 



SIMPLE DEDUCTION. 

cular change, are not studied on the retina of the eye but in 
the easier (although still obscure) cases— chemical action and 

photography. The osmotic action of cells is illustrated by 
Graham's experiments on the passage of liquids through por- 
celain partitions. The capillary circulation of the blood is 
compared to the flow of liquids in capillary tubes. Salival 
and digestion are examined by withdrawing saliva and 
trie juice from the animal body, and subjecting diffe* 
materials to their action apart. The laws of Mind, which aro 
to be carried out deductively in resolving the complicated 
situations of human beings, as in Society, are to be generalized 
from observations of the individual man in favourable situa- 
tions. For the laws of mental growth, we have to begin at 
infancy ; for the germs of moral sentiment, we refer to the 
uncivilized races.* 

3. II. Deduction proper involves two stages of com- 
plexity ; (1) The simple extension of an inductive law to 
a new case , and (2) the combination of several laws in a 
conjoint result, involving processes of Computation. 

(1) Simple Deduction is the extending of an inductive 
generalization to new cases. As in all enlargements of know- 
ledge, so in this, there is both discovery and proof. The cases 
have first to be suggested to the mind, and next to be rigor- 
ously verified by the procedure suited to the case. 

Without dwelling upon the means of suggesting new 
applications of laws, let us consider the mode of proving such 
applications. This resolves itself into a question of identity. 

Supposing that the inductive preposition 4 all matter gravi* 
tates ' has been formed upon solids and liquids, shall we apply 
it to gases ? This depends upon whether gases are matter — 
whether any property of gases is identical with the defining 
property of matter. Now, the defining property of matter is 
inertia, and gases are proved to possess this property ; whence, 
the proposition * matter gravitates* is extended to them. 
Again, Does Ether (the supposed medium of Light and Heat) 
also gravitate ? As before, we must test its identity with the 
characteristic property of matter. Now, if, as seems to Lo 
implied in the retardation of Encke's comet, the ether is 
a resisting substance, then it is matter, and accordingly 
gravitates. 

# The Arts of Discovery, brought out by scattered allusions throughout 
the work, wtil be s^ stematic llv given in Appendi < H. 
15" 



538 INDUCTION AIDED BY DEDUCTION. 

Questions of identity to establish a minor are necessarily 
part and parcel of inductive research ; but they must not be 
confounded, as they sometimes are, with the process of induc- 
tive generalization to establish a major or a general law. 
Thus, it is a moot point, whether any, and what alloys are 
chemical compounds; which must be settled by examining 
the characteristics of alloys, and comparing them with the 
essentials or characteristics of chemical combination. 

We may instance important researches that have for their 
end the proof of an identity. Thus, Dr. Andrews insti- 
tuted a series of experiments to identify Ozone (formed by 
Electricity) with the atmospheric constituent that decomposes 
Iodide of Potassium. He selected three peculiarities of 
ozone ; — (1) the power of oxidizing mercury, (2) the destruc- 
tion of ozone reactions by dry peroxide of manganese, (3) the 
destruction of its reactions at a high rate of temperature 
(237° C) ; and tried the element found in the atmosphere by 
these tests. It answered to them all. The first, however, 
(the oxidizing of mercury) is not conclusive, as other bodies, 
besides ozone, tarnish mercury. The last of the three tests 
(high temperature), answers to no known substance, except 
ozone. The three tests conjoined furnish superabundant 
evidence of the identity of the so-called ozone of the air, with 
ozone as obtained by electrolysis, and by the electrical machine. 

Another remarkable discovery of Identity is seen in Graham's 
experiments on the relations of Hydrogen to Palladium. 
There have always been chemical reasons for believing that 
hydrogen gas is the vapour of a highly volatile metal. 
Graham has contributed new evidence in favour of the 
identity. The metal palladium is capable of absorbing eight 
or nine hundred times its volume of hydrogen gas ; and, 
when so charged, is found to undergo changes in Density, 
Tenacity, Electrical Conductivity, Magnetism, relations to Heat, 
and Chemical properties. On investigating these changes, 
Graham shows that they correspond to the alterations made 
on one metal when united in an alloy with another metal ; so 
that, as far as metallic properties can be shown in such a union, 
hydrogen is metallic. The metal ' hydrogenium ' has a white 
aspect, is of sp. gr. 2, has a certain amount of tenacitv, and is 
magnetic. The cumulation of proof is all but equivalent to 
the separate production of the solid metal. 

Sir G. C. Lewis confounds the establishment of a minor, as 
* part of Deduction, with the establishment of an Inductive 
major by the method of Difference. He considers that the 



COMBINATION OF DEDUCTIONS. 

proof of a burglary in a Court of Law, or the proof thai 
Philip Francis wrote Junius, is an employment of the I 
mental or Inductive method of Difference 
Inductive methods. In reality, all such c the mak 

good of an identity to prove a minor. The kind of I). IK re- 
employed consists in bringing out successiv< 
cumstantials, to exclude by degrees cvcvy person but one'; 
and thereby to complete the identity of that one person with 
the actor in the given case. 

(2) The more difficult employment of Deduction is in the 
concurrence of different agents to a combined result ; 
when we deduce the path of a projectile from gravity, the 
force of projection, and the resistance of the air ; or the tid 
from the united action of the sun and the moon. This is the 
form of the Deductive Method, whereby we cope with the 
otherwise intractable situation called Intermixture of Elf 

Physical Astronomy will ever remain the grand exemplar 
of Deductive Investigation, as the computation of joint cam 
producing an effect. The causes can be estimated with numeri- 
cal precision, and their combined operation can be calculated 
by the higher Mathematics. In other parts of Physics, there 
are instances of the Deductive Method. The calculations 
respecting Machinery, Fluid Pressures, Motions of Fluids, 
Gaseous Pressure and Movements, Sound, Light, Heat, Elec- 
tricity, — proceed upon inductive laws, often united in their 
operation, and requiring to be computed in their joint effect. 

It has been seen, in the research on Dew, that Da I ton's 
generalization of the laws and constitution of the atmosphere 
of vapour, deductively applied, made up the wanting link in 
the experimental investigation. 

Equally telling examples of the Deductive Method may be 
culled from the recent applications of Chemistry to Animal 
Physiology. The laws of chemical combination enable us to 
trace the metamorphosis of tissue, by means of the products 
of waste. The single fact of oxidation is all-pervading in the 
animal system, and the deductions from it clear up at once 
many obscurities beyond the reach of experimental elimina- 
tion. The difficult question of Animal Heat is to a great 
extent solved already by this deductive application, and its 
complete solution will probably depend on the same method. 

We may quote farther the special applications of Chemistry, 
under the great law of Persistence, to the phenomenon of 
muscular power, of which no adequate account could be given 
by mere observation or experiment. We now know that 



330 INDUCTION AIDED BY DEDUCTION. 

muscular expenditure represents a definite combustion of the 
material of the food, although we do not know the precise 
links of the transmutation. 

When purely Inductive or Experimental proofs are sup- 
ported by reasons, or by a consideration of tbe nature of the 
case, the meaning is that Deduction is brought to the aid of 
Induction. The conclusion respecting the N. E. wind was 
confirmed by the general operation of atmospheric impurities. 
The result gained from the comparison of instances of Crystal- 
lization, is in accordance with the theoretical views of the 
two opposing molecular forces — attraction and repulsion. 
The experimental facts as to the exhaustion of the mind along 
with the body, are supported by what we know of the brain 
as the organ of the mind. Our inductions respecting despotic 
governments are aided by deductions from the laws of human 
nature. 

The applications to the Human Mind, to Character, and to 
Society, will be more fully exemplified afterwards, in the 
special chapters on the Methods of these Sciences. 

4. III. The Deductive process is completed by Verifi- 
cation. 

This applies more particularly to the Computation of 
combined causes. 

The way to verify the deductive extension of a single law to 
a new case, is actual observation of that case. We apply 
deductively the law of gravity to air, and verify the deduction 
by observing whether the air has weight. As, however, we 
may dispense with deduction when we have actual observation, 
such an instance does not show the power of the Deductive 
Method. The thing meant is, that after verifying a deduction 
by one or more instances, we shall be able to apply it to other 
instances without farther verification ; these last instances 
depending for their proof solely on the deductive process. 

When an effect is the result of several conspiring causes, we 
may deduce it from a computation of the causes ; as, for 
example, the lunar and planetary perturbations. To show 
that we have taken account of all the causes, that we have 
obtained a proper estimate of each, and that we have correctly 
computed their conjoined action, we must compare the deduced 
effects with the observed effects in a variety of instances. If 
the two precisely tally, the deductive machinery is verified ; 
if not, not. A want of accordance points to a defect in one or 
other of the circumstances quoted: — the causes or agents are 



I 



VERIFICATION OF DEDUCTIONS. 331 

not fully taken account of; their exact amount is not pre 
obtained; or the calculation of their united i 
perfect. Sometimes, the first point is defeetivo, 
residual- agent. In other cases, we know the cause hut n 
exact numerical amount; thus, in Astronomy, we 
know the relative masses of the sun,, moon, and planets, 
together with their mutual distances. Finally, it may happen 
that the calculations are impracticable. 

In Astronomy, where Deduction has gained its 
triumphs, verification has also been most thoroughly worked, 
Upwards of fifty Observatories are incessantly engaged in 
watching celestial phenomena; the observations have 
the means of perfecting the deductive operation, and making 
good all its shortcomings. 

The deductive theory of projectiles combined gravity, pro- 
jectile force, and the air's resistance ; the experiments on 
gunnery are the verification. 

The laws of the strength of materials are deduced from 
geometrical and mechanical laws, involving the size, shape, 
and position of beams, &c. ; but however certain the principles 
may appear, they cannot dispense with actual trials. 

We have supposed the verifying tests to consist of detached 
observations ; they may be furnished by groups of observa- 
tions, summed up into what are termed Empirical Laws. 
Such was the verification of Newton's planetary theory 
(founded on gravity) by Kepler's Laws. So, any theory or 
generalization of the operation of refracting surfaces on light, 
must be in consistency with Snell's law of the proportion of 
the sines of incidence and refraction. 

The formulae of fluid motions are of themselves insufficient 
to predict the facts ; experiments on the flow of rivers must 
be conjoined in a matter of so great complicacy. 

Newton calculated deductively the velocity of sound, and, on 
comparing it with the observed velocity, found a difference of 
nearly twenty per cent. It is only of late years, that the dis- 
crepancy has been got over, by a more complete view of the 
forces developed in the act of propagation. In such a delicate 
question, one verifying instance is too little. Newton himself 
squared the results by arbitrary assumptions (as the thiokqeafl 
of the air particles), which would have required for their con- 
firmation an independent class of facts. 

Very confident prediccions have been made to the intent 
that the Sun is cooling down in consequence of his enormous 
radiation ; and that the earth's rotation must ultimately decay, 



332 INDUCTION AIDED BY DEDUCTION. 

through the friction of the Tides. The data and the calcula- 
tions seem very secure in both iu stances ; yet, m order that 
the deductions may be fully established, we need evidence of 
An actual change, in past time, as regards both these moment- 
ous facts. 

Combined Induction and Deduction expresses the full force 
of scientific method for resolving the greatest complications. 
Induction alone, and Deduction alone, are equally incompetent 
to the great problems even of the Inorganic world ; still more 
so with Life, Mind, and Society. Induction, exclusively relied 
on, is called ' empiricism ; ' Deduction, without an adequate 
basis and an adequate check in the Inductive Methods, ex- 
presses the bad sense of ' theoretical," 

The two following chapters will continue the exemplification 
of the Deductive Method, of which they merely vary the 
aspect. 



CHAPTER XL 

SECOXDAEY LAWS— EMPIRICAL AND DERIVATIVE. 

1. The importance of Secondary (as opposed to Ulti- 
mate) Laws, grows out of their close adaptation to concrete 
realities. 

Speculation delights to attain ultimate generalities, which 
give the key to a vast department of nature ; as Gravity, 
Conservation, and Relativity. These are highly satisfactory 
to the mind in its craving after unity, simplicity, \ the one in 
the many/ A far more important use of these supreme 
generalities is to perfect the statement of the Secondary Laws, 
which are the more immediate guides of conduct, and the 
expression of the phenomena in their actual or concrete 
embodiment. The generalization of gravity did not supersede 
Kepler's Laws of the Planetary Motions. So long as the 
concrete fact of planetary motion has an interest for us, so 
long are we concerned with the secondary laws representing 
that fact. The use of the higher laws of Newton is to render 
these indispensable secondary laws more precise. 

The secondary laws are the ' media axiomata' of Bacon. 
They were viewed by him (too exclusively) as the steps for 
ascending to the supreme laws. Equally essential is the 



IMPORTANCE OF SECONDARE I." 

descending movement from tlie higher to the middle 

ties. No branch of knowledge is complete in 

assembled all the secondary laws that expn 

configurations of actual phenomena, and until ti odary 

laws have attained all the precision that induct; 

tion can give them. 

We formerly had occasion to remark (p. 79); with i 
to Propositions, that, like the notion, they vary in regard to 
the reciprocal properties — Extension and Compreheu 
we increase the extension, we lose comprehension, and 
versely. Now, of the two attributes, the one most imp 
for us practically is Comprehension. We have to deal 
small classes, and with individuals, and our interest lies in 
knowing the whole of the specialities attaching to these. An 
English statesman needs to know the peculiarities oi 
men. A physician has to deal with the diseases special to 
humanity, and still more those special to his own sphere ; 
while even this degree of generality, is but to prepare him for 
mastering individual cases. 

Hence, the narrowing of a proposition, which may seem a 
defect to the theorizing or speculative intellect, is the hi. 
merit in applications to practice : provided always that the 
limitation of extent is accompanied with a corresponding in- 
crease in amount of predication, that is, in meaning, connota- 
tion, or intent. The full enumeration of the properties special 
to iron, as it is found in a certain district, is essential to the 
working of that particular ore i the account of the properties 
common to all metals would be valuable merely as contributing 
a quota to the highly specialized and exhaustive knowledge 
relative to the particular substance. 

It was a frequent remark of Aristotle that the finishing 
stroke of knowledge is the tact that modifies all general pro- 
positions according to the individual case. This of course is 
in the more purely practical point of view. 

The secondary laws are either Empirical or Derivative. 

2. An Empirical Law is a uniformity supposed to be 

secondary, that is, resolvable into some more general uni- 
formities, but not yet resolved. 

That quinine cures a fit of ague is an Empirical Law. It 
is a uniformity established by experience ; it is, however, a 
secondary uniformity ; we have reason to believe that it is 



631 SECONDARY LAWS. 

capable of being resolved into higher uniformities. The pre- 
sent inability to resolve it is a disadvantage, not merely in a 
theoretical or speculative point of view, but as regards the 
application of the law in practice. 

3. When what was an Empirical Law has been resolved 
into more general uniformities, or into highest laws, it is 
termed a Derivative Law. 

The occurrence of snow on high mountains was at one time 
an empirical uniformity. It was established as an induction 
from experience, but was not susceptible of being referred to 
any higher generalizations. We can now resolve it into the 
laws connected with radiant heat passing through the atmos- 
phere. These may not themselves be the highest attainable 
generalities ; still they are much more general than the induc- 
tion connecting snow with height. 

The converting of an Empirical Law into a Derivative 
Law is a step gained both in scientific explanation, and in 
practical facilities. The defects inherent in an Empirical Law 
do not inhere to the same degree in a Derivative Law. 

4. Empirical Laws are of various kinds. Their, charac- 
ters are judged from their appearance after being resolved, 
that is, made derivative. 

I. Many are obviously made up of the combination of 
higher uniformities under definite arrangements or collo- 
cations. 

We see this class largely exemplified in the explained oi 
derived laws. The law of a projectile, Kepler's laws, the tides, 
the laws of wind and rain, the laws of geological action (igne- 
ous and sedimentary), combustion, the nourishment of living 
bodies — being formerly empirical laws, and now derived — we 
can, from them, presume the character of those that are still 
empirical. 

These combinations have been already discussed under the 
Deductiva Method. They suppose certain ultimate laws, con- 
curring in their operation, and also a certain definite arrange- 
ment and amount of the concrete agencies or forces that the 
laws refer to. 

5. II. Some secondary laws take the form of laws of 
succession between effects and remote causes ; they still, 
however, possess the character last named. 



VARIOUS KINDS OF SECONDARY LAWS. 

When a sudden shower disperses a crowd, tho ihowttl is a 
ery remote cause of the effect; a number ot Intel 
inks of causation are assignable* The taking o 
noved by a good many stages from the ran wai of Uii 
Jar strength. The sowing of a seed is followed at B 
interval with the maturing of an oak. 

This is merely a superlicial variety of the first case— com- 
bination of agents, in definite collocation. Bach one of the 
links is a distinct law of causation or coincidence, requiring 
be embodied in a definite collocation ; and the combination of 
the whole, in a suitable arrangement, is necessary to the 
result. 

6. III. Some are laws of Co-existence or of Succession 
between effects of the same cause. 

Such are the phases of the Tides, the flow of the Seasons, 
Day and Night. Here also there is the same constant circa in- 
stance — a conjunction of agents and collocations. In every 
case of a secondary law, there is, from the nature of the ease, 
more than one power at work. Only ultimate laws express 
agents in isolation, purity, or abstractness. 

In any complicated structure, a new agent produces a 
variety of changes. The taking of food leads to concurring 
alterations in almost every organ in the body- Every di.-ease 
has concurring symptoms. A country engaging in war has 
its economy simultaneously disturbed in many different ways ; 
hence there are numerous empirical statements- applicable to 
the condition of war, which are co-effects of the one general 
situation. 

7. The aggregation of properties in a natural kind — a 
mineral, plant, or animal — has something in common with 
Empirical Laws. 

As there may be uniformities of co-existence, not resolvable 
into cause and effect, such uniformities stand solely on their 
own inductive evidence, like empirical laws. They are proved 
by the method of Agreement alone, and the proof extends no 
farther than the cases observed* 

8. The criteria of an Empirical Law are principally 
these . — 

If a uniformity is established only by Agreement, it is 
not shewn to be a law of causation ; and (if not an ulti- 
mate law of co-existence) it is an empirical law. 

i 



336 SECONDARY LAWS. 

Agreement does not single out a cause when there is plurality. 
It is°at fault, besides, in discriminating cause and effect from 
effects of the same cause. Moreover, unless the variation of 
the circumstances has been thorough and complete, there is 
an uncertainty even in cases where there is but a single cause, 
and where the antecedents contain that cause. 

The Method of Difference does not at once lead to ultimate 
laws. The swallowing of alcohol is followed by a certain 
sensation ; this is proved by the Method of Difference to be 
cause and effect, yet it is not an ultimate sequence ; it is an 
empirical uniformity. 

9. The other criteria arise out of the characters already 
mentioned. 

Thus, when phenomena are obviously complicated, and 
when there are intermediate links of operation, the laws of 
such phenomena are not ultimate but secondary ; they are 
empirical, or, if resolved, derivative. 

The law that connects the fall of the barometer with wind 
or rain is plainly empirical. We can see that many different 
agencies enter into the sequence ; and, also, that there are 
many intermediate steps between the antecedent and the 
consequent. 

We presume the action of a drug to be an empirical law, 
because we know, from the complication of the human body 
and the plurality of attributes of natural kinds, that there 
must be many concurring processes, each one governed by its 
own law or laws of causation. 

LIMITED APPLICATION OF DERIVATIVE AND EMPIRICAL LAWS. 

10. A Derivative Law, and still more an Empirical Law, 
must not be extended beyond narrow limits of Time, Place 
and Circumstance. 

It being supposed that such laws are established by all the 
evidence that the case admits of, still they are applicable only 
a certain way beyond the narrow sphere where they have been 
observed to operate. 

The reasons are those already stated under the Deductive 
Method. A uniformity depending on several higher uniformi- 
ties, and on a definite collocation of agents, that" is, on certain 
special co-efficients, must fail, first, if any of the concurring 
uniformities be counteracted, and secondly, if the proper ad- 
justment of the agencies is departed from. The elliptic 



APPLICATION TO ADJACENT CAS; 

motion of the planets would bo defeated, if sot- ,]; M . 

turbing body were sufficiently near to conn lar 

attraction, or if the tangential force were made different 1 
what it is. Hence we cannot extend the law of the ell 
every body that may now or at any future time revolve al 
the sun. 

This limit to the extension of secondary laws — win 
Empirical or Derivative — is the all-important fact ivsp.r 
them, in the logical point of view. A large number of | 
vailing errors might be described as the undue extension of 
Empirical Laws. We shall present a few examples of becondafy 
laws, calling attention to the difference of our position in 
regard to them, according as they are Empirical or Derivative. 
The rise of water in pumps was an empirical law, previous 
to the discovery of the pressure of the atmosphere. The 
application of the Method of Agreement in different countr 
and with pumps of different bore, proved that no pumps could 
draw water beyond about 33 feet. The law could be relied on 
within the wide limits of place and circumstance where it had 
been tried. It could not have been extended to other planets ; 
but it might be extended, with apparent safety to any part of 
the earth. 

Since the law became derivative, the limits of its operation 
are precisely defined ; we can tell exactly where it would have 
failed. We know that on the tops of high mountains the 
maximum height would have been much below 33 feet ; that 
the exact height would not be the same at all times ; that 
other liquids, as alcohol, sulphuric acid, solutions of salts, 
mercury, vary in the height attained. Now, probably none 
of all these limitations had been actually discovered in the 
empirical stage ; they might have been obtained by sufficiently 
wide and careful experiments ; the derivation superseded the 
laborious task, which was probably beyond the competence of 
an unscientific age. 

It is an empirical law that the temperature of the eortfi 
increases, as we descend, at a nearly uniform rate of 1 of 
Fahrenheit to 50 feet of descent. This law has been verified 
by observations down to almost a mile. We might extend the 
law inferentially to the adjacent depths, as fir perhaps as 
several miles; but wo are not at liberty to extend it to the 
centre of the globe. We do not know that the requisite col- 
locations extend so far. 

Yet this law is not wholly empirical. It is a derivative 
aniformity. It is connected with the known facts— that the 

\ 



338 SECONDARY LAWS. 

earth has a high temperature in the interior, and is cooled at 
the surface by radiation in space. Knowing these, we are yet 
unable to deduce the law of decrease from the higher laws 
concerned, because we are ignorant of the degree of central 
heat, and imperfectly acquainted with the laws of its conduc- 
tion through the unknown materials of the globe. We under- 
stand the general situation, but do not possess the numerical 
and other data requisite for computing the effects. 

That air-breathing animals are hot-blooded, is a law formerly 
empirical, now derivative. It comes under the general law of 
the dependence of temperature on the oxygenation of the blood, 
and may be extended widely on the faith of that great 
generality. 

The Law of Continuity — ' Natura non agit per saltum ' — is 
an Empirical Law. In the continuity of Vegetable and Animal 
Life, there would be, under the Doctrine of Development, a 
reason for the fact, and it would be in that case Derivative. 
Also, in the transition from one state of matter to another, — as 
in melting, boiling, and their opposites — there must be a 
certain amount of continuity owing to the greatness of the 
transition. But except where there is some presumption of 
this nature, the extension of the law is wholly unsafe ; we are 
not to expect, for example, that the simple bodies of nature 
should be arranged in series with continuous or shading pro- 
perties. We find the greatest gaps in almost all the properties 
of the elementary bodies. 

In medical science, there is hardly such a thing as a single 
effect produced by a simple cause. What is worse, there are 
scarcely any great inductive generalities relating to the cure of 
disease, except through hygienic or constitutional treatment. 
Thus the use of drugs is almost exclusively empirical. 

The limitation in this case operates variously. It forbids 
our inferring that two medicines of close kindred will have 
the same effect ; thus bark and quinine are not interchange- 
able, although the one is the crude form and the other the 
essential extract. It also forbids our extending a mode of 
treatment to a closely allied ailment, as in reasoning from 
one species of fever to another. Lastly, it forbids the applica- 
tion of the same treatment to the same disease, in different 
persons. 

Hence, medicine is of all sciences the one most completely 
tentative. Experience gives a probability to begin with ; but 
until the effect is tried in the new case, we cannot, as a 
general rule, rely on it. 



EMPIRICAL LAWS IN MEDICINE. 

Until the day arrives when the operation of mediant 
made derivative, the only progr 
multiplied experience, a more exact statement of the condi 

attending on the successful application of certain 
treatment; as tor example, the constitutional orothi I 
stances in the patient favourable or unfavourable to special 
drugs. 

The treatment of tape worm by male' fern is of old date in 
medicine. In the early period, the failures were frequent ; 
at present, the oil of the fern is extracted and given instead of the 
root, with an almost uniform success. This empirical unifor- 
mity is to a certain extent derived or explained ; the substance 
is a poison to the parasite. After such an explanation, there 
is afforded a clue to other remedies for the disease ; previous 
to the explanation, the uniformity was confined to the one 
remedy. 

As an empirical law in Medicine, we may instance Blight's 
discovery of the connexion between albuminous urine, and 
degeneration of the kidney. The law is as yet unresolved 
into any higher law of structure and function ; the kidney 
degeneration is not associated with degeneration in any other 
tissues of the body ; and no account is given of the temporary 
production of albumen without the permanent disease. 

It is an empirical law that about 250 persons in a year 
commit suicide in London. This law may be extended a little 
way into the future, but it may not be extended into a remote 
time, when moral habits may be different, nor to other cities 
and populations. 

The Statistics of Mortality show a remarkable coincidence 
between the rate of mortality and the density of the popula- 
tion. A high degree of longevity is found in thinly peopled 
districts, notwithstanding even the poverty that sometimes 
occurs in sterile tracts ; and mortality reaches its maximum 
in the most crowded parts of cities. If we knew nothing of 
the causes of this uniformity, if it were as empirical as the 
medicinal action of mercury on the system, we could not 
extend the law into other countries and other circumstances of 
the population. But it is a derivative law, and knowing what 
agents the effect depends on, and what circumstances would 
defeat their operation, we apply it without scruple to every 
portion of the human race. We should, however, refrain from 
applying it to animals very differently constituted from man 
as to the necessities of breathing pure air. All animals require 
oxygen, but some need it in smaller quantity, and are indif- 

a 



34:0 SECONDARY LAWS. 

ferent to impure gases ; while warmth and the opportunities of 
better food might more than compensate for the close atmos- 
phere of a confinel habitation. 

In regard to the Human Mind and character, we have 
uniformities that cannot be extended to the race generally. 
Tims, the universality of sympathy or fellow-feeling is liable to 
exceptions. Mr. Samuel "Bailey, after quoting, from a travel- 
ler in Burmah, the incident of a drowning man being beheld 
by a crowd as an amusing spectacle, and being allowed to 
sink without an attempt at succour, makes the following 
remarks : — 

' Incidents of this kind (and the example might be easily 
parallelled from other nations) serve to show that when we 
ascribe certain sentiments to human nature or to men univers- 
ally on given occasions, because they exist amongst ourselves 
on those occasions, it is by no means a safe inference ; we 
cannot safely ascribe them except to men under analogous 
circumstances of knowledge and civilization. 

1 We may attribute with confidence to most men and to most 
races of men, the rudimentary feelings which I have shown to 
originate and to constitute moral sentiment ; and some of them 
with equal confidence to all men : namely, sensibility to cor- 
poreal pleasure and pain ; liking the causes of one and dis- 
liking the causes of the other ; the propensity to reciprocate 
both good and evil ; the expectation of the same reciprocation ; 
and more or less sympathy with other sensitive beings ; but 
the direction and intensity of these emotions respectively it is 
often difficult and even impossible to assign : there are so 
many causes at work to counteract, or modify, or suppress 
such of these common susceptibilities as can be counteracted, 
or modified, or suppressed — to call them forth or to keep 
them in, that, unfurnished with precise knowledge of national 
and social circumstances, we cannot predict with confidence 
how they will manifest themselves on particular occasions. 
Without specific information of this kind we cannot safely 
pronounce that the people of rude or distant and imperfectly 
explored countries would, under given circumstances, share in 
those affections and moral sentiments which it seems contrary 
to our own very nature, under such circumstances, not to have/ 

That l the mind of man is by nature conciliated and adapted 
to his condition ' was formerly an empirical law. We may 
now consider it as a deduction or derivation from the law of 
Universal Relativity. The principle has been greatly abused. 
It has been loosely extended far beyond the limits where it is 



POLITICAL RULES. ;; \ \ 

observed to hold true ; indeed those limits were n ootlv 

marked in its empirical state. As a derivative uniformity, wt 
may assign its limits with tolerable precision. 

The laws of Political Society are all secondary laws, either 
empirical or derivative. Hence the necessity for limit 
application. The politician is, like the ancient sailor 
to sail close by the shore, rarely venturing out of sight of land. 
We are not at liberty to transfer to our own time the maxims 
suitable to the ancient world, supposing even that the ancients 
really attained any political rules highly salutary in their own 
case. 

1 The distinction between ancient and modern history,' saws 
Mommsen, * is nomere chronological convenience. Modern 
History is the entry on a new cycle of culture, connected 
at several epochs of its development with the perishing or 
perished civilization of the Mediterranean States, but destined 
to traverse an orbit of its own.' It would be a vicious extension 
of secondary laws, to predict the extinction of modern nai 
because the great ancient empires are perished. 

We cannot transfer at once the practice of one nation to 
another nation. Hardly any political device has been so much 
copied as the British constitution. Yet, its advantages being 
not purely empirical, but to a certain extent derivative, it may 
be extended to adjacent cases with some confidence. 

It is suitable to the complicacy of the political structure to 
make changes in the direction of existing institutions, and to 
confide in them only when introducing a state of things n 
adjacent to the present. After seeing the working of a ten- 
pound franchise in this country, the inference was fair that 
the lowering to eight, seven, or six pounds could not depart 
very far from actual experience. 

The use of precedents in Law and in Politics exemplifies the 
rule of limitation. Bacon, remarking on legal precedents, lavs 
it down that the more recent are the safer, although, on the 
other hand, they have a less weight of authority. 4 A prece- 
dent is at its maximum of proving force when it is suiliciently 
near our own time to ensure similarity of circumstances, and 
sufficiently distant to ensure the consolidation of practice, and 
the experimental exhibition of the practical result.' (G. C. 
Lewis). 

11. The rule may be farther illustrated under the second 
form of the Secondary Laws— Uniformities of remote 
connexion between cause and effect. 



312 SECONDARY LAWS. 

Of these, the most prominent examples are the results of 
slow processes in the arts, protracted treatment in disease, the 
growth of plants, the development of animals, the formation of 
the human character. That all empiricisms of this class must 
be precarious and liable to frequent defeat is apparent. Even 
when derivative to the full extent, they are rendered uncertain 
by the number and complication of the agencies. 

12. Lastly, with reference to Uniformities suspected or 
known to be effects of a common cause. 

The principle of limitation is still the same. 

As an example, the case is put — what reliance are we to 
place on the sun's rising to-morrow ? 

Suppose, in the first place, that this were an empirical 
generality, we being ignorant of its derivation. Suppose, 
also, that we have authentic evidence that the sun has risen 
daily for the last five thousand years. How far into the future 
are w T e at liberty to extend the law ; to what limits of time 
should we confine it ? The answer is, w T e may count the con- 
tinuance in the future, on the same scale as the continuance 
in the past ; we may fairly assume a period counted by 
thousands of years ; we may be tolerably certain for one 
thousand years, and have a considerable probability, for three, 
four, or five thousand ; but we should not be safe in extending 
the scale to tens of thousands, still less to hundreds of 
thousands. For anything we should know, a catastrophe may 
be preparing that will speedily interfere with the regularity of 
day and night ; still, long continuance in the past reduces, 
without annihilating the chances. 

Let us next look at the case as a derivative uniformity. We 
know that the phenomenon will continue so long as these 
circumstances are conjoined, namely, (1) the luminosity of 
the sun, (2) the earth's being within a proper distance of the 
sun, (3) the earth's rotation, and (4) the negative condition of 
the absence of any intervening opaque body to act as a screen. 
Now, we know from past experience that all these conditions 
are likely to be perpetuated for a period of time, to be estimated 
by not less than hundreds of thousands of years. The sun 
may be cooling, but the rate, judging from the past, is 
extremely slow ; the earth's rotation is believed to be subject 
to decay, but the rate of decay is infinitesmally little; 'the 
removal of the earth out of the solar influence is in opposition 
to our very best guarantees ; and the permanent intervention of 
an eclipsing body is the most unlikely incident of all. Thus, 



INDUCTION OF CAUSE. 

then, while, as an empirical law, wo cannot well extend 
rising of the sun (or day and night as we now ha 

thousands of years at most, we may extend it, as a den. 
law, to hundreds of thousands, if not to millions. 

EVIDENCE OF THE LAW OF CAUSATi 

13. It may be shown that the Law of Causation, the indi- 
spensable grouud work of all Induction, itself iv; 
the highest evidence suitable to the case— uiKjontr.id 
Agreement through all nature. 

We have hitherto taken for granted that sufficient evidei 
of the only kind suited to the case, has been obtained in favour, 
of the law of Universal Causation, on which law have been 
grounded all the processes of experimental elimination. A 
sammary of this evidence will farther illustrate the logical 
processes detailed in the foregoing chapters. 

The uniformity of successions was first observed in easy 
instances, such as the more obvious mechanical effects.. A 
body at rest was observed never to move from its place without 
the application of some force to move it; a body in motion 
was observed not to stop abruptly without interference and 
obstruction. The fact of the descent of unsupported bodies 
is invariable. So light and heat display obvious regularities 
that could be counted on. Even in the instability of the winds 
there would be discovered circumstances of constancy. The 
most complicated of all things, living bodies, were seen to 
have numerous points of striking uniformity. 

That change of every kind whatsoever follows on a definite 
prior change, could not be affirmed in early times, except by 
the mere instinct of generalization, which is no proof. Hence 
in ancient philosophy, there were alternative suppositions. 
Aristotle allowed an element of Chance, along with the reign 
of Law. 

Modern science has extended the search into natural se- 
quences, collecting new examples of uniformity, and rem >ying 
exceptions and apparent contradictions. Investigations have 
been pushed into every department of nature; and had there 
been any decisive instances where change grew out of 
or where the same agent, in the same circumstances, was not 
followed by the same effect, such instances must have been 
brought to light. 

14 In the form of Persistence of Energy, under definite 



54.4 EVIDENCE OF THE LAW OF CAUSATION. 

laws of Collocation, the Law of Cause and Effect has been 
subjected to the most delicate experimental tests. 

By irrefragable observations it was shown that Matter is 
indestructible, which is one element of nature's constancy. 
Farther observations have proved the numerical Persistence 
of Force throughout all its transformations, and also the unifor- 
mity of the collocations or arrangements for transferring it. 

The first contribution to this result was the proof of tho 
Laws of Motion, as respects both the continuance of motion 
once begun, and the conservation of the total moving force in 
case of transfer by impact. These mechanical verities make 
up one department of uniform cause and effect. Next came 
the proof of the equivalence of mechanical force and heat — 
the constancy of the amount of one produced from a definite 
amount of the other. Joule's mechanical equivalent of Heat 
testifies to nature's constancy in a very wide department. 
Following on this is the mumerical estimate of the heat of 
Chemical combinations, also admitting of numerical statement, 
from which there is no deviation ; a third great department 
of constancy is thereby established. 

If numerical equivalence has not been arrived at in Nerve 
Force, and in Light, the subtleties of the phenomena are 
sufficient to account for the deficiency. We have reasonable 
ground to presume that, according as these phenomena are 
fully understood, they will show the same constancy as all the 
rest ; the burden of proof lies upon any one maintaining the 
contrary. 

The only exception usually claimed to the Law of Causation 
is the alleged Freedom of the Will. But whatever be the 
mode of dealing with this long-standing enigma, there is a 
statistical testimony in favour of the constancy of human 
motives. The actions of men have a degree of regularity 
compatible only with uniform causation. 

Mr. Mansel has characterised as a * paralogism ' the doc- 
trine that ' the ground of all Induction is itself an Induction.' 
He might have called it & paradox or an epigram, an apparent 
contradiction needing to be resolved: it is not a paralogism 
unless it can be made out a self-contradiction. 

If the account given above of the methods of Proof and 
Elimination is sufficiently intelligible and conclusive, nothing 
farther is necessary to resolve the paradox. There is one fun- 
damental mode of Proof— Agreement through all nature— by 
which all ultimate laws are established, including Causation. 



CAUSATION BESTS OX AGREEMENT ALoNK. 

There are several derivative, deductive, ordependenl 
of Proof, the special Methods of Elimination A 
(according to Mill's Canon), Difference, and Variations; these 
are called by courtesy Inductive Methods; they are more 

properly Deductive Methods, available in Inductive • 
tious. The special form of Agreement described in the i 
is not quite the same as the fundamental method of A 
ment, on which alone repose all the ultimate generaliza! 
That canon, as supposing Causation, would be inappiicab 
the proof of Causation. The method of Agreement that w 
Causation is not a method of elimination." It does not pr< 
by varying the circumstances, and disproving Bucce 
antecedents ; it can only find A followed by a, wherever the 
two occur. Until the law is first proved, we eannot i 
A as the cause of a, by omitting successively B, C, I), and all 
other accompanying circumstances, leaving nothing constantly 
joined save A and a ; even if this were done, there must still be 
a search through all nature for A followed by a, when the qnei 
tion of causation itself is at issue. Hence Agreement for estab- 
lishing an ultimate law is not the same as the Method of 
Agreement, in Mill's canon, for establishing cases of causation, 
after the general law is sufficiently guaranteed. 

There is a certain propriety in comparing the establishment 
of the Law of Causation (or any other ultimate law), with the 
proof of an Empirical Uniformity, which has nothing but de- 
tailed Agreement to found upon. True, an Empirical Uni- 
formity is to be applied only a little way beyond the limits of 
time, place, and circumstances. But, now, as Mr. Mill 
remarks, ■ if we suppose, the subject matter of any generaliza- 
tion to be so widely diffused, that there is no time,, no place, 
and no combination of circumstances, but must afford an 
example either of its truth or its falsity, and if it be never 
found otherwise than true, its truth cannot depend on any 
collocations unless such as exist at all times and pla< 
can it be frustrated by any counteracting agencies, unle 
such as never actually occur. It is, therefore, an empii 
law, co-extensive with all human experience; at which i 
the distinction between empirical laws and laws of nal 
vanishes, and the proposition takes its place among the i 
firmly established, as well as largest truths accessible u> 
science.' 






CHAPTER XII. 
EXPLANATION OF NATUEE. 

1. The laws arrived at by Induction and Deduction are 
the proper Explanation of natural phenomena. 

Explanation has various meanings. These all agree in 
affording us a certain satisfaction or relief when oppressed 
with the difficulty, obscurity, perplexity, contradiction, mys- 
tery, of natural facts. Bat the human mind has at different 
times been satisfied in different ways ; and individuals still 
vary as to the kind of explanation that satisfies them. 

When all Nature was peopled with deities, and the various 
phenomena partitioned among them, a sufficient explanation 
of anything was that a certain god or goddess willed it. The 
intervention of Neptune was a satisfying account of why a 
storm arose. The wrath of Apollo was the explanation of the 
plague that broke out among the Greeks at the siege of Troy.* 

There is a special and every-day form of explanation that 
consists in assigning the agency in a particular occurrence ; 
as when we ask — what stops the way ? who wrote Junius ? 
who discovered gunpowder ? These questions belong to our 
practical wants and urgencies, but the answer does not involve 
the process of scientific explanation. If, however, we proceed 
from the 'who' or 'what' to the ' why :' — why does A's 
carriage stop the way ? why did the author of Junius write 
so bitterly ?. — there is an opening for the higher scientific 
process. 

2. The basis of all scientific explanation consists in 
assimilating a fact to some other fact or facts. It is 
identical with the generalizing process, that is, with In- 
duction and Deduction. 

Our only progress from the obscure to the plain, from the 
mysterious to the intelligible, is to find out resemblances among 
facts, to make different phenomena, as it were, fraternize. 
We cannot pass out of the phenomena themselves. We can 
explain a motion by comparing it with some other motion, a 

•Bee Grote's Plato (Phadon) fcr the views of the ancient philosopher* 
with regard to Explanation, or the Idea of Cause. 






EXPLANATION IS GEXKKAUZATION. 

pleasure by reference to some other pleasure. We do Hoi 
change the groundwork of our conception of tl 
merely assimilate, classify, generalize, concent* 
to unity, a variety of seemingly different bhingB. 

The phenomenon of combustion was considered to 1. 
been explained when Priestley showed it to be tbe combina- 
tion of oxygen with carbon or other substance^ in s^ti, be 
assimilated the fact to cases of oxidation, as the formal i< 
the red precipitate of mercury, the rusting ot iron, 
Lightning was explained by Franklin's assimilating it 
electricity. The polarity of the needle was explained by 
assimilating the entire globe to a magnet or loadstone. 

Explanation thus steadily proceeds side by side with 
assimilation, generalization. Combustion was explained by 
oxidation; oxidation is explained by the higher generality — 
chemical combination ; chemical combination is swallowed up 
in the Conservation of Energy. 

3. Mr. Mill distinguishes three forms of the explanation 
of facts and laws. 

I. Explaining a joint effect, by assigning the la vs of 
the separate causes, as in the ordinary Deductive operation. 

The Deduction of a complex effect, by computing the sum 
of the separate elements, is also the explanation of that effect. 
By combining gravity with projectile impulse, we explain 
the motions of the planets. This deduction once verith 
offered as the explanation of the planetary motions. In other 
words, the showing that these motions are made up of this 
two causes — gravity and tangential force — is the explaining 
of their motions. 

In such cases, the explanation points out the simple oai 
concurring, in the shape of forces or agencies, and also indi- 
cates their amount and their due concurrence. Jupiter's 
orbit depends on the mass of the sun, on the tangential force 
of the planet, and on its mean distance from the sun. 3 
are, in the language of Astronomy, the coefficient*, which i 
be given in order to our assigning the result of the operation 
of the laws. A mere law, such as the law of gravity, i 
an explanation until it is clothed in the oon< 
two or more gravitating masses, with a given amount I 
given distance from each other. These numerical Bti 
the coefficients of Astronomy, are also said to dcic-rnin.. 
collocations of the agents concerned. 



348 EXPLANATION OF NATURE. 

To explain the rise of a balloon, is to give the laws of 
gravity, of buoyancy, ancf of gaseous elasticity, and to state 
the exact weight and elasticity of our atmosphere, and the 
specific gravity of the mass of the balloon. 

To explain genius is to refer it to general laws of the mind, 
or to certain elementary powers— intellectual and emotional — 
whose higher or lower degrees and modes of combination 
produce the kind of intellectual superiority so named. 

To explain the rise of free governments is to state the 
general principles of human action, and the definite collocation 
of circumstances calculated to produce the effect. 

The separate laws are obviously more general than the laws 
of the conjoint effect. Gravity has a much wider sweep than 
planetary motions ; the law of the perseverance of moving 
bodies in a straight line is far more comprehensive than 
tangential impulse. 

4. II. Explanation may assume the form of discovering 
an intermediate link, or links, between an antecedent and 
a consequent. 

What seems at first sight the direct or immediate cause of a 
phenomenon may, by the progress of assimilation, turn out 
the remote antecedent. The drawing the trigger of a musket 
is followed by the propulsion of a ball. The ivhy of this 
phenomenon is given by disclosing a series of intermediate 
sequences, each of which is assimilated with some known 
sequence. The trigger by concussion evolves heat ; the heat 
ignites the gunpowder; the gunpowder is a mass adapted for 
very rapid combustion ; the combustion evolve gases which, 
being confined in a small space, have a very high expansive 
force ; the expansive force propels the ball. 

Again, the contact of sugar with the tongue is the pi^ecursor 
of a feeling of the mind, the sensation called sweetness. The 
explanation, so far as hitherto attained, supplies the following 
series of closer links. The sugar is absorbed by the mucus 
membrane of the tongue, and comes in contact with the fila- 
ments of the gustatory nerve ; there ensues a chemical or 
some other molecular action on the nerve. This action is 
of a kind that can be propagated along the course of the nerve 
to the nerve centres, or the brain ; whence are diffused a multi- 
tude of nervous currents ending in muscular movements. To 
the cerebral agitation attaches the mental state called the sensa- 
tion of sweetness. 






INTERMEDIATE LIN 



The unexplained phenomena connected with the Li 
Conservation refer to the intermediate links, 
the interchange of the mechanical and the! moleonta 

and of one molecular force with another. The mole* 
i in the conversion of mechanical energy into I 
into electricity, chemical force into muscular DO* 

nervon3 power, — are not accounted for: and w 

beginning and an end where we have i 

there must be various intermediate s 

being assigned and brought under some general law of c . 

tion. 

The intermediate links, or sequences, are each one 
than the combined sequence. Take the case of a sw. 
The absorptive power of the animal membranes for various 
substances (the crystalloids of Graham) is a general Lav* 
which the action in tasting is merely one example or 
tion. The molecular disturbance from the contact or I 
and sugar is but a case of chemical or molecular affinity. 
The current action of the nerve force is a limited ins 
current actions ; the electrical forces exhibit oth i 
the whole being comprehensible under some higher law. 
Finally, the link that relates the physical actions of the brain 
with the mental effect belongs to some wider statement that 
relates mental states generally to their physical cone 

As observed, in the previous chapter, it is incident to such 
many-linked sequences, to be more frequently frustrated tliau 
the simpler sequences that make them. A ciremn&J 
counteracting any one of the closer links counteracts the 
whole phenomenon. If the lock of the musket i D in- 

sufficient concussion of the explosive substance; if the 
powder is rendered incombustible by damp ; if the expan 
gases burst the piece : — in any one of these contingencies, the 
ball is not propelled. 

5, III The third mode of Explanation is ten 
Subsumption of one law into another ; or the _ 
of several laws in one more general and all-compn 
law. 

This represents the upward march of gr- 
and simple. We have attained a certain num. er of mi 
generalities, by assimilating individual casea in 
duction. We have assimilated the kindling 
and for light and for the disintegration oi - 
one head, called combustion ; we have af 



350 EXPLANATION OF NATUBE. 



inffi and corrosion of metallic surfaces under another head 
we subsume both under the higher law of oxidation, which 
both exemplify. We have also assimilated the action of acids 
upon alkalies under a general head: we find that this case 
can fraternize with the foregoing and with many other 
phenomena, under a still higher, or more general aspect, 
signified by chemical combination. 

So, aoain, terrestrial gravity and celestial attraction, each 
tbe result of separate assimilations, being found to agree, are 
subsumed into the illustrious unity of Universal Gravitation. 

Magnetism, Common Electricity, Voltaic Electricity, 
Electro-Magnetism, &c, are all strung upon the common 
thread of Electrical Polarity. 

Capillary attraction, solution, alloys (not chemical), cements, 
&c, are subsumed under the general law of molecular attrac- 
tion (not chemical) between different substances, named 
heterogeneous or alien attraction. 

Kumerous laws of smaller compass are subsumed under 
Relativity. The pleasures of variety and novelty, the neces- 
sity of contrast in works of art, antithesis in rhetoric, the 
statement of the obverse or counter proposition in science, — are 
minor laws generalized, but not superseded, by the higher 
law. 

When minor laws are thus merged in a greater law, the 
mind feels a peculiar and genuine satisfaction — the satisfaction 
of having burst a boundary to expatiate over a wider field. 
We rise from a statement bearing upon a small group of facts 
to a statement comprehending a much larger group ; from a 
ten-fold condensation, we reach a thousand-fold condensation. 
The intellect, oppressed with the variety and multiplicity of 
facts, is joyfully relieved by the simplification and the unity of 
a great principle. 

The charm of resolving many facts into one fact was acutely 
felt by the speculative minds of antiquity. It took a power- 
ful hold of the earliest Greek philosophers ; and made them 
almost unanimous in imagining that all phenomena whatso- 
ever are at bottom one, or are susceptible of being represented 
in some single expression, being merely the many-sidedness of 
some single central power, substance, agent, or cause. Such 
unity was, according to Thales, Water ; according to Anaxi- 
mander, an Indeterminate Substance ; according to Anaxi- 
nienes, Air ; according to Pythagoras, Number. 



. 



ULIMATE niENOMEXA. 
LIMITS OF EXPLANATION. 

6. Scientific explanation and inductive generalization 
being the same thing, the limits of Explanation are 

limits of Induction. 

Wherever Induction (extended by Deduction) can g 
legitimate scientific Explanation can go, they being- the 
process differently named. 

7. The limits to inductive generalization are the limits 
to the agreement or community of facts. 

Induction supposes similarity among phenomena, and when 
such similarity is discovered, it reduces the phenomena under 
a common statement. The similarity of terrestrial gravity 
to celestial attraction enables the two to be expressed as one 
phenomenon. The similarity between capillary attraction, 
solution, the operation of cements, &c, leads to their being 
regarded not as a plurality, but as a unity, a single causative 
link, the operation of a single agency. 

So remarkable have been the achievements of modern times, 
in the direction of lofty generalities, that some countenance 
seems to be lent to the ancient dream of attaining an ultimate 
centralized unity in the midst of the seeming boundless 
diversity of nature. 

It depends purely on actual investigation, how far all 
phenomena are resolvable into one or into several ultimate 
laws ; whether inductive finality leaves us with one principle, 
with two, or with twenty principles. 

Thus, if it be asked whether we can merge gravity itself 
in some still higher law, the answer must depend upon the ; 
Are there any other forces, at present held distinct I 
gravity, that we may hope to make fraternize with it, so I 
join in constituting a higher unity ? Gravity is an attra 
force ; and another great attractive force is cohesion^ 01 
force that binds together the atoms of solid matter. Might 
we then join these two in a still higher unity, expresi 
a more comprehensive law? Certainly we mi-lit, bur 
to any advantage. The two kinds of force agree in the 
point— attraction, but they agree in no other; indeed, in 
manner of the attraction they differ widely; so 
we should have to state totally distinct laws 
is common to all matter, and equal in amount in equal 111 
of matter whatever be the kind; it follows the law u! the 
16 



352 EXPLANATION OF NATURE. 

diffusion of space from a point (the inverse square of the 
distance) ; it extends to distances unlimited ; it is indestruc- 
tible and invariable. Cohesion is special for each separate 
substance ; it decreases according to distance . much more 
rapidly than the inverse sqnare, vanishiug entirely at very 
small distances. Two such forces have not sufficient kindred 
to be generalized into one force ; the generalization is only 
illusory ; the statement of the difference wonld still make two 
forces ; while the consideration of one wonld not in any way 
simplify the phenomena of the other, as happened in the 
generalization of gravity itself. 

A^ain, gravity, considered as a power to pnt masses in 
motion, to generate visible or moving force, may be 
compared, by way of an attempt at assimilation, with the 
equally familiar mode of begetting motion by impact, or the 
stroke of a mass already in motion ; as in propelling a ball by 
a mallet. Here too, however, we have, with similarity of 
result, a total contrast in the mode. Gravity draws bodies 
together from a distance ; impact must be supposed to urge 
them through their atomic repulsions. When the expanding 
gases of kindled gunpowder blow a bullet through the air, 
there is no actual contact of the parts ; there is merely the 
operation of powerful forces of mutual repulsion, acting, 
however, at very short distances, like the cohesion of solidity. 
Now, there appears to be nothing in common to gravity and 
these atomic repulsions, except the result. We have, there- 
fore, no basis for assimilation or inductive generalization in 
such a comparison. The two modes of action must be 
allowed to lie apart in physical science ; they must be em- 
bodied in different statements or laws, with no hope of being 
ever brought together. 

It is because gravity does not assimilate with the propnlsion 
of impact from a blow or a stroke that people have acconnted 
it mysterious. In point of fact, there is no more mystery in 
the one than in the other. Attraction, from great distances, 
is one form of the production of force ; Repulsion, at near 
distances, is another form. The last of the two is, on the 
whole, most familiar to us; it is the genus that our own 
physical force belongs to ; and we, by a mere whim, suppose 
it a simpler and more intelligible mode of exerting power ; 
the truth being that, in all that regards simplicity and intel- 
legibility, gravity has the advantage. It is only by confining 
ourselves to the superficial glance of bodies coming into close 
contact, thence giving and receiving momentum, that we 






ULTIMATE FEELINGS OF THE MINI). 



suppose this mode of exerting force a simple one; the i 
pointed links of molecular repulsion are much more 
cated than gravity. 

A similar line of remarks would -apply to any endearon 
assimilate gravity with the Correlated Forc< 
forces by their nature counteract gravity. The various n 
ments in nature are explicable by the conflict and mutual 
action of two great Powers; Gravity, on the one I 
and the sum total of the Correlated Forces, molar and i 
cular on the other. The Correlated Forces mostly a; 
under the guise of repulsions, as, for example, hi : urh 

so that this must be considered their typical mani, 
the electrical and magnetic attractions are exceptional, ami 
are probably mere superficial aspects of the deeper fact of 
repulsive separation. 

Three departments of Force thus stand out so distinct B 
be incapable of assimilation : — Gravity, the Correlated Fc 
and Molecular Adhesion. This last appears under two 
forms; — the attraction between particles of the same sub- 
stance — iron for iron, water for water ; and the attraction 
between two substances — as iron for lead, w r ater for alcohol or 
for common salt. There may be a possibility of generalizing 
these two, or stating them as a common force. Some approach 
has been made to this in the fact that the second kind of 
attraction holds between bodies nearly allied — as metals with 
metals, earths with earths. 

8. The ultimate laws of Nature cannot be less numerous 
than the ultimate feelings of the human mind. 

This, as Mr. Mill pointed out, is the insurmountable 1 b 
to generalization, and consequently to explanation. What 
number of distinct states of consciousness, not mutually re- 
solvable, can be traced in the mind, there must be thai 
of ultimate facts or elements of knowledge, and of ultimate 
laws connecting those states with their causes or col C 
If the sensation of colour be radically distinct from th< 
of resistance, of movement, of form, there must be e 
law with reference to colour. The phenomenon called v. 
ness cannot be resolved into the phenomenon 
motion. 

Even if we found that the fact of whiter 
by a certain molecular structure, and certain m< 
ments, we should not thereby resolve whiteness into D 
the facts would be distinct facts, although joined 



35i EXPLANATION OF NATUKE. 

So, we are aware that the sensation of sound is conditioned by 
a vibratory movement of the particles of a sounding body ; 
but the vibration is not the sound ; all we can say is that a 
law of causation relates the vibration to the sound. Now 
there must always remain one law connecting the molecular 
movements of bodies with the sensation of whiteness, and 
another law connecting molecular movements with the sensa- 
tion of sound. 

In so far as all sensations are generalized into a common 
fact of sensation, having similarity with diversity, so far may 
we generalize the laws that connect sensation with corporeal 
activities. This is a real and important step of generalization. 
Yet it does not supersede the necessity of other laws for con- 
necting special and irresolvable modes of sensation with their 
special seats of corporeal activity. We may have a law of 
pleasure and pain generally ; yet we need laws for the distinct 
modes of pleasure and pain — the pleasures of light, of sound, 
&c. — inasmuch as these cannot be resolved into each other. 

The great generalities relating to Force all refer to one 
sensibility of our nature — the muscular, or the active side ; 
owing to which fact, they may admit of unity of law, or a 
common statement. Likewise, there may be unity of law as 
regards Light and Colour, provided all the modes and varie- 
ties are resolvable into the variation in degree of some funda- 
mental mode of consciousness. If there be several fundamental 
modes, there must be a law for each ; thus there may be 
wanted one law for white light, with its degrees, and one for 
each of the primary colours — four laws for the sense of sight. 

We may be able to discover how Heat causes Light to the 
extent of generalizing the molecular condition of luminosity, 
and connecting this with the molecular condition of high 
temperature ; but that such molecular condition and its ac- 
companiments — radiation, refraction, &c. — should yield the 
sensation of light, must always be expressed in a distinct law, 
a law uniting an objective with a subjective experience. Such 
is the proper goal or end of our knowledge in regard to the 
phenomenon. 

FALLACIOUS AND ILLUSORY EXPLANATIONS. 

9. One form of illusory explanation is to repeat the fact 
in different language, assigning no other distinct yet 
parallel fact. 

This is ridiculed in Moliere's physician, who gives as the 
reason why opium causes sleep, that it has a soporific virtue. 

1 



ILLUSION OF FAMILIARITY. 

Not much is done to explain the gri f 

plants by saying that it is due to a Bubstance nam. d 
phviL' The only step gained is the fact (if ii I 
greenness in all plants is due to the -ice. 

A simile is sometimes offered lor an e 
Latent Heat was merely a re-statement of the fact : he □ 
have gone on to call it secret, concealed, embodied, Bhu 
Heat; all which expressions would merely i 
stance that a certain amount of heat no longer 
heat to the sense, or to the thermometer. 

It is with the great ultimate generalizati (ho 

Uniformity of Nature, and the Axioms of Mat! 
we are most prone to give as a reason, i mere 

various wording of the principle itself 'Why must the 
future resemble the past? ' * Because Nature is Uniform. 1 

The phenomenon, sleep, was referred by Whewell I 
of periodicity in the animal system. This, however, 
nothing but repeat the fact to be explained ; fcber 
assimilation with another fact, so as to yield a hig 
rality, which would be inductive explanation, and no refei 
to a higher generality already formed, which would be (i> 
tive explanation. A step towards real explanation is made by 
comparing it with the repose or quiescence of the orf 
after any activity whatsoever. This is to assimilate the 
phenomenon with another distinct phenomenon ; the two taken 
together form a higher generality, which, so far as it go. 
an explanation. 

10. Another illusion consists in regarding phenomena 
as simple because they are familiar. 

Very familiar facts seem, to stand in no need of expbm:* 
themselves, and to be the means of explaining what 
be assimilated to them. 

Tims, the boiling and evaporation of a liquid is supposed to 
be a very simple phenomenon requiring no ex; 
a satisfactory medium of the explanation of r;irer pi 
That water should dry up is, to the nnin mind, a I 

wholly intelligible; whereas, to the man acquaint 
Physical science, the liquid state is anonr 
The lighting of a fire, by contact wit 
scientific difficulty; yet few people think it 
bubble is a conflux of unexplained phenol 
action, from familiarity, has long been reckoned so I 



35G EXPLANATION OF NATUPwE. 

itself as to have provided a satisfactory explanation of all 
other modes of generating mechanical force. 

11. The greatest fallacy of all is the supposition that 
something is to be desired beyond the most generalized 
conjunctions or sequences of phenomena. 

It is supposed by many that the possession of a supremo 
generality on any subject is insufficient ; the mind, it is said, 
craves for something deeper, and this craving (which can 
never be satisfied) is considered to be proper and legitimate. 
The generalization of Gravity leaves behind it a sense of 
mystery unsolved, as if there were something farther that we 
might arrive at if obstacles did not intervene. 

jSewton seemed unable to acquiesce in gravity as an ulti- 
mate fact. It was inconceivable to him that matter should 
act upon other matter at a distance, and he therefore desired 
a medium of operation, whereby gravity might be assimilated 
to Impact. But this assimilation has hitherto been impracti- 
cable ; if so, gravity is an ultimate fact, and its own sufficing 
and final explanation. 

The acceptance of the law of universal gravitation as a full 
and final solution of the problem of falling bodies, without 
hankering or reservation, is the proper scientific attitude of 
mind. There seems no hope at present of making it fraternize 
with a second force, and there is no other legitimate out^oim* 
of enquiry with reference to it. 

In the same way the mysteriousness often attributed to 
Heat, is partly resolved by the Theory of Correlated Forces, 
under which heat is assimilated to movement. The subjec- 
tive fact of heat — the sensation of the mind so described, is a 
fact coming under the general relationship of body and mind. 

Light is still a mystery in the legitimate sense ; it has been 
but imperfectly generalized as regards its physical workings. 
Every isolated phenomenon is, in the proper acceptation, a 
mystery. 

Apparent contradiction is something that demands to be 
explained ; investigation should never stop short of the attain- 
ment of consistency. Thus, the glacial period of the earth's 
history, is at variance with the only hypothesis yet framed as 
to the solar agency — the slow but gradual cooling in the course 
of ages. 

The molecular aspect of the Correlated Forces is repulsion 
(as in Heat), yet in Magnetism and in Friction Electricity, it 
appears as attraction. 



MYSTERY OF BODY AM) MINI). 

Free-will is often stated as a hopeless and insoluble a I 
diction. To leave any problem m such q 
scientific. 

The union of Body and Mind lias Long been c 
mystery by pre-eminence. The prevailing opii 
that this connexion would for ever resist and paralyze 
tion. Yet, the scientific mode of dealing with the i 
clear. The material properties and the mental propertie 
each to be conceived according to their own nature —the 
by the senses, the other by seif-consciou6ne>> . We fcbei 
deavour to assimilate and generalize to the utmost each i 
of properties ; we generalize material properties into in 
gravity, molecular forces, &c. ; we generalize mental pr 
ties into pleasures, pains, volitions, and modes of inte 
We next endeavour to rise to the most general laws of the 
union of the two classes of properties in the human and an 
organization. When we succeed in carrying this generalising 
operation to the utmost length that the case apj Innt 

of, we shall give a scientific explanation of the relationship of 
body and mind. Any farther explanation is as incomp- 
as it is unnecessary and unmeaning. 

Such langruaofe as the following is unscientific : — * C 
sensation is a fact, in the constitution of our corp* 
and mental nature, which is absolutely incapable of 
tion.' The only meaning attachable to this is, that bodily 
and mental facts are fundamentally distinct, yet in i 
alliance. So — 'To this day, we are utterly ignorant 
matter and mind operate upon each other.' Properly B] 
ing there is nothing to be known but the fact, general]* 
the utmost. 

* Is there' says Hume * any principle in all nature more 
mysterious than the union of soul and body ; by 
supposed spiritual substance acquires such inflnenc 
material one, that the most refined thought is able t 
the grossest matter ? ' 

Again, 'we know nothing of the obj 
compose the universe; our observation of external D 
limited to the mutual action of material objed 
What is the good of talking of a snpposabi 
sible, knowledge ? * 

♦ See Ferrier s Remains (vol. II. p. 430), for g,mc 1 1 I *>"* 

on the nature of Explanation. 



CHAPTER XIII 

HYPOTHESES. 

1. Various meanings belong to the word Hypothesis. 

I. It means the suppositions,, suggestions, or guesses, as 
to any matter unknown, leading to experimental or other 
operations, for proof or disproof. 

In the course of a research, many suppositions are made, 
and rejected or admitted according to the evidence. Kepler 
made an incredible number of * guesses as to the planetary 
relations before he discovered the actual laws. Davy sup- 
posed the alkalies to be compounds before he established the 
fact by decomposing them. 

In the Inductive operation of arriving at general laws, the 
supposition made is some law that appears likely to explain 
the fact, as Kepler's Third Law (of periodic times and mean dis- 
tances). Such suggested laws have to be duly verified 
according to the Experimental Methods. 

In the properly Deductive operation of carrying out a law 
by bringing cases under it, the supposition is an identity, as in 
the examples already given under the Deductive Method. 
The hypothesis of a man's being guilty of a certain crime is of 
this nature ; the proof consists in the tallying or fitting of the 
circumstances of the accused with the circumstances of the 
crime (commonly called ' circumstantial evidence '). Of the 
same nature is ' the hypothesis of Wolfe with respect to the 
origin of the Homeric poems ; the hypothesis of Niebuhr, 
with respect to the derivation of portions of the early Roman 
history from ballads or epic poems ; the hypotheses of Eich- 
horn, Marsh, and others, with respect to the origin of the text 
of the four gospels ; the hypothesis of Horace Walpole, with 
respect to the character of Richard the Third, and various 
hypotheses with respect to the Man in the Iron Ma ski So 
there are hypotheses, in literary history, as to the authorship 
of certain works, as the Aristotelian (Economics, the treatise 
De Imitatione Christi, the Letters of Junius, In each of these 
cases a supposition is made, the truth of which is tried by 
combining it with all the circumstances of the case.' 






A HYPOTHESIS DEFINED. 



These cases contain no mailers for logical disci] 
do not raise the questions that attach to the LJndulai 
thesis of Light, the Development Hypothesi . 

Theory, and other celebrated hypotheses. 

2. The definition of a Hypothesis (according to U 

a supposition made (without evidence, or with in 
evidence of its own) in order to deduce conclu 
agreement with real facts ; the agreement being the | 
of the hypothesis. 

Hypothesis, in this sense, is a defective kind of proof; T 
is some missing link; and the question is raised, hu\v shall 
this be made good in other ways. 

For example, in the geological investigation concerning the 
transport of erratic boulders, there are various possible su 
sitions — icebergs, glaciers, water currents. Now, we m 
unable to get what we should desire, in accordance with the 
strict course of experimental elimination, namely, proof of the 
actual presence and operation of one or other ofth< 
The only resource then, is to compare the appears 
with what would result from the several modes of ac 
If these appearances are consistent with one mode only, there 
is a certain strong presumption in favour of that one. The pre- 
sumption would obviously amount to certainty, if we have 
had before us (what we cannot always be sure of having) all 
the possible or admissible agents. 

In the absence of proof as to a man's real motives, on a 
given occasion, we often decide in favour of some one. 
the man's conduct is exactly what that motive would die 
The soundness of the criterion depends upon there beinj 
other motive or combination of motives that would haw 
same effects. 

3. It is manifestly desirable, in assumptions relatin 
natural agencies, that these should be known to ex ; 
Hypothesis is then limited to such points as— ti 
sence, their amount, and the law of their operation. 

Such are the hypotheses as to the erratic boold 
may ascribe an epidemic to excessive heat, to mo 
electricity, to magnetism, to animalcules, to bad 
crowded dwellings, or to some combination of 
agencies are real; every one of them is wh.v 
ivera causa. What is hypothetical is the actual pretanoi of 



3G0 HYPOTHESES. 

one or other, the mode of operation, and the sufficiency to 
produce the effect. If all these could be established in favour 
of one, the point would be proved. If the presence cannot bo 
proved (the difficulty in past effects), there must be shown an 
exclusive fitness in some one to account for the appearance. 

The illustrious example of Gravity may be quoted in its 
bearing on Hypotheses. Newton's suggestion was, that celes- 
tial attraction is the same force as terrestrial gravity. He 
thus proceeded upon a real or known cause ; the hypothetical 
element was the extension of gravity to the sun and planets. 

The preliminary difficulty to be got over was the rate of 
decrease of the force according to distance. From Kepler's 
laws, it was proved that celestial attraction diminishes as the 
square of the distance increases. Was this true of the earth's 
gravity ? The foil of the moon was the criterion, and exactly 
coincided with that supposition. Thus, then, the law of the 
sun's attraction and the law of the earth's attraction are the 
same. The earth's attraction extends to the moon ; may ii 
not extend to the sun, and may not the sun reciprocate the 
very same attraction ? 

The wonderful amount of tallying or coincidence in this 
case was sufficient in the minds of all men. to justify the 
assumption that the two attractions are the same. The 
hypothesis was proved by its consequences. And, as no rival 
supposition has ever stood the same tests, the Newtonian 
theory is considered as beyond the reach of challenge. 

The rival hypothesis to gravity, in the explanation of the 
celestial motions, was the Cartesian vortices, or whirlpools of 
ether, which floated the planets round, as a chip revolves in 
an ecldy of a stream. 

The identity here assumed is between the circular motion 
of the planets, in what is commonly supposed to be empty 
space, and the circular motion of a whirlpool of water or of 
air. 

The first obvious disparity respects the fluid medium. In 
the whirlpool of water we have a liquid mass with density 
sufficient to buoy up wood, and mechanical momentum suffi- 
cient to propel it in the direction of the stream. No such 
fluid mass is known to be present in the celestial spaces ; the 
very supposition is hostile to all familiar appearances. A 
fluid sufficient to move the planets at the rate they move in 
would have numerous' other consequences that could not 
escape detection. It would mix with our atmosphere as an 
active element and produce disturbances on the earth's surface. 



ASSUMPTION OF A NEW Ac: 

In this vital circumstance, therefore, the compari 
assimilation is incompetent. 

• A second disparity was brought to light in N 
tisxn of the scheme. The laws of a whirlpo< 
of the planetary orbits ; a whirlpool is incorapal i the 

laws of Kepler. Now, we cannot assimilate i oical 

phenomena, two attractions, for example, unless tb 
the same law of force. This is a vital point in a me 
comparison. The following of the same dynamical 
the crowning circumstance of the likeness bel 
solar force. 

It would be said, therefore, that the Cartesian scheme 
not assign a vera causa. It assigned, no doubt, a 
action quite familiar to us; whirlpools are a real ft 
it assumed a material substance unlike anything hitherto 
covered; water we know, and air we know, but the e 
demanded for the vortices is entirely foreign to all our experi- 
ence of material things. 

4. As it would seem irrational to affirm that we air 
know all existing causes, permission must be given to 
assume, if need be, an entirely new agent. The conditions 
of proof are, in this case, more stringent. 

The chief example of this kind of Hypothesis is the 
Undulatory Theory of Light. 

The supposition of an etherial substance pervading all B\ 
and by its undulations propagating Light and Heat, as tl 
propagates sound, is in accordance with many of the facts of 
Light, more especially what is called the Interference of J. 
a generalization of many distinct appearances. The hypo 1 1 
also served to discover new facts of luminous agency. 

Assuming what is not strictly accurate as yet, that the 
undulatory hypothesis accounts for all the facts, we ere celled 
on to decide whether the existence of an undulating ether is 
thereby proved. 

We- cannot positively affirm that no other v. ill 

explain the facts ; what we can say is, that of all the by] 
hitherto suggested, this approaches the no. 
explanation. ISewton's corpuscular hypotlu 
have broken down on Interference ; and there is 
day, no rival. 

Still, it is extremely desirable in all snch b; fad 

some collateral confirmation, some evidenco aliunde, or 
supposed ether. This is supplied in part by the observations 



3G2 HYPOTHESES. 

on the comet of Encke. If the retardation of that comet, and 
other observations of a like nature, establish the fact of a 
resisting or inert medium, there will remain, as hypothetical, 
the properties of that medium, namely, the peculiar mode of 
elasticit y titled for transmitting luminous and other emana- 
tions. 

There is farther to be urged, in support of the hypothesis; 
its constancy with the other hypothesis that regards Radiant 
Heat and Light as the propagation of molecular movements 
from hot and luminous bodies. The transmission of these 
influences through space, by the communication of molecular 
impulse, is in harmony with their character as motions in the 
molecules of the masses of ordinary matter. 

An additional confirmation is supplied in the remarkable 
fact that bodies, when cold, absorb the same rays (of the solar 
spectrum) that they give out when hot. This is precisely 
analogous to the law of musical strings, namely, that, of the 
notes sounded by another instrument in their neighbourhood, 
they assume each its own note. 

5. Some Hypotheses consist of assumptions as to the 
minute structure and operations of bodies. From the 
nature of the case, these assumptions can never be proved 
by direct means. Their only merit is their suitability to 
express the phenomena. They are Representative Fictions. 

All assertions as to the ultimate structure of the particles of 
matter are, and ever must be, hypothetical. Yet we must not 
discard them because they cannot be proved ; the proper cri- 
terion for judging of their value is their aptness to represent 
the phenomena. That Heat consists of motions of the atoms 
can never be directly shown ; but if the supposition is in con- 
sistency with all the appearances, and if it helps us to connect 
the appearances together in a general statement, it serves 
an important intellectual function. 

The phenomena of the solid, liquid, and gaseous state of 
matter can be represented by the opposing play of two sets of 
forces—the attraction of cohesion inherent in the atoms of 
each substance, and the repulsive energy generated by the 
heat motions. In crystals, the heat motions are at a minimum, 
and in that case, the cohesion assumes a polar character, or is 
concentrated at particular points, whose difference of relative 
situation makes difference of crystalline form. 

The Undulatory hypothesis of Light, even although it may 
never be fully established as fact, will have a permanent valuo 



REPRESENTATIVE FICTIONS. 

as a "Representative summary of the facts o 
be gradually carried to perfection in this ch 

In a paper by Graham, on the ' Molecular Mobility o 
published in the Transactions of the Lloyal Socii 
there is put forward a hypothesis of the Constiti^ti 
Matter. The assumptions are these : — 

(1) The various kinds of matter may consist, of one 

of Atom or molecule, having a different kind of moveraei 
each substance. This is in harmony with the equal 
gravity upon all bodies. 

(2) The greater the energy or swing of the primordial nod 
inalienable movements of the ultimate atoms, the lighter the 
mass. The leading fact named Density or speeiiie gravity is 
represented by this assumption. 

(3) These ultimate molecules, whose primitive movement 
gives specific gravity, are supposed to be made up in gro 
each group having a farther movement, vibratory or other; 
which second superinduced movement represents fche 
molecule affecte'd by Heat, and leading to gaseous expansion. 
This Graham also calls the diffusive molecule. 

(4) Equal volumes of two forms of gaseous matter, irre- 
spective of w r eight, have a facility of combining ; ties is 
Chemical Combination. It is a hypothetical expression of fche 
law connecting Atomic Weight with Gaseous Volume. The 
gaseous state is expressed by Graham as the typical state of 
matter; * the gas exhibits only a few grand and simple fea- 
tures. 1 

The special point of the hypothesis consists in assuming 
motions within motions, like primary and secondary planets. 
There is no limit to the successive groupings and their chi 
teristic movements. For still more complex properties, new- 
groupings may be assumed. 

A somewhat different hypothesis of Molecular Motions 
been given by Mr. Clark Maxwell (Phil. Trans. 1866). It 
might be superadded to Graham's. 

Under the methods of Chemistry, we shall advert to 
hypothesis named The Atomic Theory ; and under the 
of Biology, there will cccur other examples of celebi 
hypotheses. Also, in the Logic of Medicine, tl 
tive conceptions are bronght under review. 

The political fiction as to a Social Contract, 
the rights of sovereignty, is not entitled to the 
Hypothesis. It is a pure fabrication to serve B 



3d HYPOTHESES. 

even a party purpose ; and ranks with the legends in the 
ancient Grecian states, relied on as giving validity to the 
title of a tribe to its territory, or of a family to the sovereign 
power. 

6. It has been said (by Dugald Stewart and others) 
that the reasonings of Geometry are built upon hypotheses. 
The meaning is, that the figures assumed are abstractions, 
or ideals, and do not correspond to any real things. 

The word * hypothesis/ is here employed in a somewhat 
peculiar sense. It is identical in meaning with ' Abstract,' as 
opposed to actual or ' Concrete ' objects. The important 
truth intended to be conveyed would probably be given much 
better by avoiding the use of * hypothesis.' 

In Geometry, as in all Abstract Reasoning, the essence of 
the operation is to view the things in one exclusive aspect, or 
with reference to one single property, although, in point of 
fact, no object exists possessing that property in pure isola- 
tion. The geometrical Point is a mark of position ; we reason 
upon it solely as marking position. Every real point, and 
even the point that we conceive in the mind, possesses at the 
same time a certain magnitude, a certain colour, and certain 
material substance. We. however, make abstraction of all 
these features ; we do not assume them in any degree ; we 
drop them entirely out of view ; we consider * position/ in 
so far as 'position/ and make affirmations on that special 
assumption. When we come to deal practically with an 
actual point, we must re-admit all these properties belonging 
to it in its concreteness ; we must allow for the fact that no 
actual point can determine an abstract position ; it covers an 
area, and therefore does not fix position except by an approxi- 
mation. 

In Mechanics, there are convenient fictions that subserve 
the abstract reasonings of the sciences ; as, for example, the 
supposition that the whole mass of an irregular body is con- 
densed into its Centre of Gravity — an operation impossible in 
fact, but having a practical convenience in mechanical demon- 
strations. It is desirable, for certain purposes, that we should 
make abstraction of the form and size of a mass, and view 
only its weight and its relative position to some other mass ; 
and one way of compassing the end is to imagine the form and 
the size non-existent, or that the mass exists in a mathe- 
matical point. We say there is a certain definite position in 
the interior of the earth, wherein, if the whole mass were 



EXrEUIMENTUM CBUCIS. 

concentrated, the earth's attraction for tho sun and 
would be the same as it actually is. This is merely b 
aid to the process of reasoning in the Abstract, Thi 
is applicable to all the other abstract centres — oscilla 

suspension, gyration, &c. 

7. A fact that decides between two opposing Bypotheses 

was called by Bacon an experimentum en 

The 'Instantia Crucis ' of Bacon does not properlj 
to the Experimental Methods of Induction, li is the 
instance between two contending hypotheses. Thu 
the Copernican s\^stem was brought forward in opposition lio 
the Ptolemaic, not only was there a necessity for showing that 
the new system corresponded with all the facts ; there 
farther required the production of some facts that it B 
could conciliate. The first fact of this decisive character was 
the Aberration of Light, a fact incompatible with the earth's 
being at rest. ' Another fact, equally decisive, is furnished by 
the recent pendulum experiments of Foucault with regar 
the motion of the earth. Bacon himself, who never fully 
accepted the Copernican system, desiderated an * experimen- 
tum crucis' of this nature, namely, a fact to show that the 
velocities of bodies appearing to move round the earth arc 
in proportion to their distance ; which, he says, would be a 
proof that the earth stands still, and that the aj^parent daily 
motion of the stars is real. 

The entire absence of mechanical enercry in tho rnv 
light is regarded as decisive against Newton's Em: 
Hypothesis. The most delicate experiments fail to show any 
moving energy in the concentrated rays of the sun ; which 
failure is inconsistent with a stream of particles of inert matter. 



CHAPTER XIV. 

APPROXIMATE GENERALIZATIONS AND PROBABLE 

EVIDENCE. 

1. Probable Inference is inference from a pi 
only approximately true. 

Every certain inference supposes that the major 
position universally true, as ' all men are mortal,' ' all n 



366 APPROXIMATE GENERALIZATIONS. 

gravitates/ When a minor is supplied to such propositions, 
the conclusion is certainly true. _ * 

From a proposition true only in tlie majority of instances, 
the inference drawn is not certain, but only probable. 'Most 
(not all) pbenogamous plants have green leaves;' hence it is 
probable that any given class of these plants has green leaves. 

The word for such generalities is ' most ; ' the synonyms are 
'many/ 'usually,' ' commonly, ' 'generally,' ' for the most 
part/ ' in the majority of instances.' 

2. If we know the exact proportion of cases in an ap- 
proximate generalization, we can state numerically the 
degree of probability ot an inference drawn from it. 

It being known that a certain thing happens in nine in- 
stances out of ten, the probability, in a particular case, is nine 
to one, or nine- tenths. All the metals, except copper and 
gold, are devoid of colour, (being either white or some shade 
of grey). The probability that a new metal is white or grey 
is as fifty- two to two. 

On the supposition that the majority of drunkards are never ■ 
reformed, the probability is against the reform of any indivi- 
dual drunkard. The strength of the probability depends upon 
our estimate of the comparative numbers. If this estimate is 
vague and uncertain, — if we cannot say w T hether the reformed 
drunkards number one fiftieth, one twentieth, or one-fourth of 
the whole, — our estimate of the probability in the given in- 
stance is correspondingly vague. 

What Hobbes says of Charles II — 

Nam tunc adolescen3 
Credidit ille, quibus credidit ante Pater — 

is true of the vast majority of men even in the most enlightened 
countries. Hence a strong probability that any given indi- 
vidual has never exercised any independent judgment in 
politics or in religion. A hundred to one is a safe estimate of 
such a probability. 

It is an approximate generalization that both intelligence 
and independent thought are most frequent in the middle 
ranks of society. The generalization has in its favour deduc- 
tive as well as inductive evidence. We know the circum- 
stances adverse to those qualities in the highest, and also in 
the lowest, ranks. Still, it is but approximate, and yields 
only probability in every giveu application. Like all proba- 
bilities, however, if applied to masses, it gives certainty. The 






PROBABLE INFERENCES. 



ctisre action of a middle class body would be more inf 
je»t and independent than the action of the oilier cla 

The proposition is approximately true that the wealth 
nore virtuous than the indigent. There are numerou 
ions, but the evidence is suilicient to prove (he rule as an 
approximate generalization. The only dispute i the 

?xtent of it. Direct statistics on the great scale are wan! 
md the deductive argument consists in comparing the I 
:ncies for and against virtue in the wealthy, as comp 
with the poorer class — a comparison where, from the \ 
nature of all estimates of human conduct, a certain latitude of 
expression must be allowed. 

The characters of men are described by such general terms 
as energetic, timid, tender-hearted, irascible, truthful, intel- 
lectual, and so on. Even when most carefully generalized, 
these characters are only approximate ; they represent prevail- 
ing tendencies, liable to be defeated in the complicacy of 
human motives, So with classes, professions, and nations. 
All the current generalities respecting the characteristic 
sex and of age are mere approximations. Literary and Art 
criticism, as expressing the style and manner of authors or 
artists, is of a like nature. 

The operation of laws and institutions is at best but 
approximate. We cannot affirm that the general good con- 
sequences follow in every instance. The tendency of severe 
punishments is to deter from crime ; they may do so in nine 
cases out of ten, or ninety-nine out of a hundred. It is the 
duty of the state to seek ont the mode that approximates 
most to the desired end. In such a case, statistics give a kind 
of numerical p*ecision to the general tendency, and a corres- 
ponding exactness to the inference of probability. 

The very best institutions have to be defended on tho 
ground of superior good, not of absolute or unexceptional 
good. This is all that can be said for liberty as against re- 
straints, for responsible government as against despotism. 

Proverbial sayings are for the most part but rude appi 
nations to truth. Many of them can hardly be said to 
a preponderance of cases on their side. * The more i 
less speed ' is not true in the majority of instances ; its i 
is chiefly as an epigrammatic denial of the univ. 
rule that activity succeeds in its object. We often 
in parading the'exceptions to approximate generalil 
not a few of our proverbs are occupied with the n 
of minorities. Tallyrand's * No zeal' is inc ralej 



3G8 APPROXIMATE GENERALIZATIONS. 

the rule that it crosses, however, is but approximate, and ha* 
exceptions ; the point of the saying lies in suggesting these. 

3. It is a legitimate effort to endeavour to make the 
approximation of a rule as close as possible, before apply- 
ing it to cases. This can be done in various ways. 

(1) An approximate generalization is rendered absolutely 
certain in its scope, when all the exceptions can be enumer- 
ated ; as in grammar rules, and in Acts of Parliament contain- 
ing schedules of exceptions. 

(2) A very near approximation can be made if we know the 
exact occasions and circumstances where the rule holds. Thus 
that * Honesty is the best policy ' is in the abstract only a 
rouo-h generalization ; it is far from the exact truth. But we 
are able to assign the specific circumstances where it holds 
good more nearly. The * honesty ' should exactly correspond 
to the standard of the time, not rising above, and not falling 
below the established code. It should be apparent and not 
concealed from view. It should contribute something to the 
advantage of persons of weight and influence. Thus limited 
and qualified, the approximation is very near the truth ; yet 
not altogether true. The dishonest successful men are still 
sufficiently numerous to constitute a standing exception to the | 
maxim. 

The Proposition c Knowledge is virtue ' was maintained in 
the Socratic school. It is an appproximate generalization, 
giving a certain small probability in its applications. That it 
has the truth on its side is proved by the statistics of crime ; 
the majority of criminals coming from the least instructed 
part of the population. Still, the exceptions* are numerous. 
We know from deductive considerations that virtue does not 
spring directly from the knowing faculties ; the filiation is in- 
direct or circuitous. The best application of so slight a pro- 
bability is to take it with concurring probabilities. The 
conditions of a virtuous character can be stated with consider- 
able precision, while intellectual culture also is an element 
whose value can be assigned. Hence, in applying the rule to 
a known case, we can infer with a far higher probability, than 
could be given by any one approximate generality, as to the 
virtuous tendencies of knowledge, of parentage, of occupation, 
and other circumstances. We can unite all the presumptions 
into one still stronger. 

It is a usual defect of empirical generalities that the sub- 
ject of them is badly defined, or that the circumstances where 



INCREASED APPROXIMATE 

the predicate holds cannot be exactl; , ig a 

common "defect in the practico of medicine. A drag has a 
certain efficacy in the majority of instances, ami is | 
only probable in its consequences. A higher 
would give the exact conditions wherein it succeeds, v. 
would be to convert the approximation into certainty. 

So in Politics. Certain institutions, as for example I 
Government, are good for nations generally. In some c 
they fail. It is for political science to specify accurate! . 
circumstances where they are suitable, and those where they 
are unsuitable ; by which means we may attain to rules of a 
certain, or nearly certain character. 

It is commonly said that being educated at a public school 
developes particular manly virtues, as self-reliance, courage, 
&c. This is but an approximate generalization. U we had 
the comparative numbers of the successes and the failures 
could assign the probability in a given instance. Still be! 
however, would be the enquiry, what are the circumsta 
Avherein the effect would arise ; what kind of youths wuu 
operated on in the salutary way ? 

It is an approximate generalization that absolute so 
abuse their power ; it is true, in a large majority of instai 
but not in all instances. It can be converted into a still closer 
approximation, if we can assign the particular situation of an 
individual sovereign — the motives operating upon him per 
ally, either as encouraging or as checking the despotic \ 
Hence, by a series of provisos (as Mr. Mill remarks) we 
render an approximate rule, an almost certain rule : — An 
absolute monarch will abuse his power, unless his position 
makes him dependent on the good opinion of his subjects, or 
unless he is a person of unusual rectitude and resolution, < r 
unless he throws himself into the hands of a minister p nes- 
ting these qualities/ 

4. Approximate generalizations give an opening 
bias of the feelings, and to the arts of a sophistical 1 

It is impossible to deal fairly with an approxi- 
mation, except by forming some estimate, the I 
be had, of the instances on one side and on the othe 
is often difficult even to the most candid and paii 
truth-seeker. Nothing then is easier than to turn 
mind from a part of the instances, and to decide 
remainder. Any strong feeling has this him 
For example, our Patent Law has raised a certain numb 



370 ANALOGY. 






persons to wealth ; it has stimulated a certain number to 
inventions, whether profitable or not to the inventors; it has 
induced a certain number to waste their lives in unproductive 
and hopeless enterprises : it has obstructed, in certain instances, 
the introduction of improvements. Whether the law has 
been good or evil on the whole, depends upon the relative 
member of these various instances. Now, it would be most 
difficult to attain an exact comparative estimate in such a ques- 
tion. How easy then for any one to incline to the instances 
favouring a preconceived theory, and to pay no heed to the rest ? 
The arts of the pleader suit themselves to this situation. 
By dwelling upon and magnifying the instances in one side, 
by ignoring and explaining away those in the other, a skilled 
advocate reverses the state of the numbers in the approximate 
generalization, making the minority seem the majority. Tho 
reply needs to be conducted so as to redress the distorted 
estimate. (For the practical applications of Probability to 
Testimony and other Evidence, see Appendix I.). 



CHAPTER XV. 

ANALOGY. 

I. The foundation and justification of all inference is 
Similarity. The similarity may exist in various forms' 
and degrees, and the validity of the inferences will be 
modified accordingly. 

When two situations are exactly the same, the uniformity 
of nature leads to the same consequences. Place equal weights 
in a balance so as to make an exact equipoise. Shift the 
centre of motion to one end, and that end will rise and the 
other fall, every time that the change is made. A great deal 
of variety may be introduced into the experiment, with the 
same result. The rod may vary in length, and in material, 
and the weights may be small or great : so that we may have 
sameness in the result without sameness of the antecedents. 

Again, having seen a great many animals die, we infer that 
other animals living and to be born will die ; the resemblance, 
together with nature's uniformity, being the justification. 
But there are often wide disparities between the instances 
observed and the instances inferred. 



INDUCTION IN DIFFERENCE Of B 

It was, however, the object of the I i | s to 

eliminate the 

la the m 
experiment with the b il 
metL .: the one 

remove the poinl 
in the beam ; that the size 
and material of the wei< 

animal life; the fact called 01 life is th 

tpanied with mortality ; the f 

r being vertebrate or invertebrate, are ::. \j eliiuiu- 

1 as unessential. 
An inductive inference is thus an inference from samen^ 

iculars, shown by induction to be the particulars 
always present when some consequence or co 
sent. This is an inference by identity, a perfect induct. 

2. There may be a radical difference in the 
two compared phenomena without preventing a strict 
• ductive inference. The sole condition is he same- 

ness apply to the attri ind by indu c the 

consequence assigned. 

To say * there is a tide in the affairs of men* is to m 
mere metaphor, the subjects compare! being t binct. 

a from one subject to another of a different k 
might be called reasoning by An yet, the inference 

might be such as to deserve the name of induction. G 
the difference between the march of human history, 
the flow of the tides, still, if the two phenomena exactly re- 
sembled in the single feature of ebbing and flowing, and if no 
inference were drawn, except what this feature involved, the 
adornment would be a sound and strict inducth n. If hi. 
affairs in any way are truly describable as ebbing and flo* 

e entitled from one movement to predict the : 
I: periods of great public excitement in special topics as 
Liberty, Religion, aggressive War, are folk l3 °f 

apathv, there is a species of r iM movement, and tl. 
the tides may so far be applied to the case, by 
induction, or else by a deduction founded on an indi 

The Chinese p md their 

rnal principle, and to justify their peculiar form ol 
ism on the similarity of the state to a family 
is not inductive ; there is a failure in essential p 
crude metaphor. There is a certain important til 



372 ANALOGY. 



namely, the fact of government, involving authority, superior- 
ity, and punishment ; and any inferences drawn upon this 
single circumstance would be valid. Certain of the merits 
and of the dements of government are identical in both 
instances ; the graduation of punishment to offence, consist- 
ency and fairness on the part of the ruler to the ruled, are 
equally required in the family and in the state. But it is not ! 
an inductive inference to say that because the parent is 
despotical, so should the state. The two cases do not agree 
in the point whence the despotical relation flows ; in the 
family, the subjects of government are children ; in the state, 
the subjects are grown men, on a level with the rulers. The 
inference would require the case of a very ignorant and 
degraded community ruled by a wise and high-minded caste. 
To whatever degree a nation approximates to this state of 
things, there is an identity between it and the family relation- 
ship. 

Plato's comparison of the state to an individual man is not 
an analogy in the proper sense of the term. It is one of those 
figurative resemblances where the points of agreement and of 
disagreement are perfectly ascertainable, and where there is 
no element unknown. Any one can tell whether the inferences 
drawn from the comparison follow from the points of agree- 
ment. That there should be a three-fold classification of 
citizens in the state, cannot be inferred or confirmed by an 
analysis of the mind into three leading functions. The con- 
stitution of a state has nothing in common with the divisions 
of the mental powers of an individual man. 

The same remark is applicable to another favourite com- 
parison of Plato's — virtue to health. The resemblance is 
exceedingly slight ; yet, if nothing were inferred but what 
grew out of that resemblance, we could not object to the use 
of the comparison. But Plato's theory of punishment derived 
from it supposes a likeness that does not hold ; and the theory 
is refuted by exposing the dissimilarity. 

The Ancient Philosophy was full of these misapplied com- 
parisons, improperly termed analogies. 

Speaking with reference to the early growth of Law, Mr. 
Mayne observes : — ' Analogy, the most valuable of instru- 
ments in the maturity of jurisprudence, is the most dangerous 
of snares in its infancy. Prohibitions and ordinances, ori- 
ginally confined, for good reasons, to a single description of 
acts, are made to apply to all acts of the same class, because 
a man menaced with the anger of the gods for doing one 



PROPER ME.VNING OF ANALOGY. 

fching, feels a natural terror in doing any other thing retni 
connected with it. After one kind of food has been inl 
for sanitary reasons, the prohibition is extended to all 
resembling it, though the resemblance occasionally depends on 
analogies the most fanciful. So, again, a wise provision 
insuring general cleanliness dictates in time long routine 
ceremonial ablution ; and that division into classes which 
particular crisis of social history is necessary for the main- 
tenance of national existence degenerates into the most d 
trous and blighting of all human institutions — Caste. 1 

Analogy has been often defined 'resemblance in relatioi 
as when a wave of water is said to be analogous to an undu- 
lation of air, or of ether; or a magnet is compared to a 
charged Leyden jar because of the common polar condition. 
This definition is objectionable chiefly on the ground of 
vagueness. The word 'relation' is too general for a preriso 
statement of the case. What truth or fitness there is in the 
expression can be given in other ways. 

3 Analogy, as different from Induction, and as a dis- 
tinct form of inference, supposes that two things from 
resembling in a number of points, may resemble in some 
other point, which other point is not known to be con- 
nected with the agreeing points by a law of causation or 
of co-existence. 

If two substances agree in seven leading properties, ami 
differ in three, the probability of their agreeing in some 
eleventh property (not known to be connected with any of the 
ten) is, with reference to the known properties, seven to time. 
But this rule would be modified by the consideration of tho 
number of properties still remaining to be discovered, a cir- 
cumstance necessarily indefinite. If we had reason to sup 
that a large number of properties still remained undiscovered, 
the probability could not be stated with the same fixity or 
confidence. 

4. An argument from Analogy is only Probabl 
probability is measured by comparing the numl 
importance) of the points of agreement with the mi 
and importance of the points of difference 
also to the extent of the unknown propel 
with the known. 

No Analogy can amount to full proof; very 1 
a high probability. ' It may afford,' says Reid, k 



STi ANALOGY. 

less degree of probability according as the things compared 
are more or less similar in their nature ; but it can afford 
only probable evidence at the best/ 

The natural Kinds afford the best examples of the typical 
case of Analogy. They have numerous properties, known 
and unknown; extensive agreements prevail among groups 
of them, together with differences more or less numerous. 
Thus, sodium and potassium have numerous points of agree- 
ment, and a few points of difference. There would, therefore, 
be a certain amount of probability that any effect due to 
sodium, or a given compound of sodium, might arise from 
potassium, or the same compound of potassium. 

The celebrated guess of .Newton, as to the Diamond, which 
was afterwards verified by experiment, was not an analogical 
inference in the strict sense. Had the inference been from a 
single body, as an oil, to the diamond (the point of agreement 
between them being unusual refracting power), the resem- 
blance would have been too limited even for a guess. The 
application to the Diamond was the carrying out of an 
Empirical Law, partially, if not wholly proved. The circum- 
stance that arrested Newton's attention was that the refracting 
power of bodies is very nearly as their densities excepting that 
unctuous and sulphureous bodies refract more than others of the 
same density. Having obtained measures of the refractive 
powers of the densities of twenty-two substances, varying in 
density between air and diamond, he found that they fell into 
two classes. In one class, were topaz, selenite, rock- crystal, 
Iceland- spar, common glass, glass of antimony, common air : in 
all which, the refracting powers are almost exactly as the 
densities, excepting that the refraction of Iceland-spar is a 
little more than the proportion. In the second class were 
camphor, olive oil, linseed oil, spirit of turpentine, amber, which 
are, 4 he said,' ' fat, sulphureous, unctuous bodies,' and diamond 
which ' probably is an unctuous substance coagulated ; ' all 
these, compared together, have their refractive powers almost 
exactly proportioned to their densities. But now, when the 
two classes are compared, the refractive powers of the second 
class (the unctuous substances) are twice or thrice as great, 
in proportion to their densities, as the refractive powers of the 
first class. Water has a middle position between the two 
classes ; salts of vitriol may stand between the earthy sub- 
stances and water; and spirit of wine between water and the 
oils. ^ The suggestion as to the diamond thus arose from its 
position among a number of highly refracting bodies thafc 



EXAMPLES OF ANALI Q V. 

igreed in being of an inflammable or combust il)lo nature. 
The concurrence of nigh refracting power with inflammability 
was an empirical law ; and Newton peroeiving 
extended it to the adjacent case of the diamond. Thi 
is made by Brewster that had Newton known the r 
powers of the minerals greenoclcite and octohedrite^ ho would 
have extended the inference to them, and would ha 
mistaken. 

As an example of Analogy proper Ictus suppo- 
of Peru to possess certain properties, medicinal or ol 
Suppose next, that the balsam of Tolu agrees in a groat number 
of these, but differs in one or two important or unimportant 
properties. On this proposition, we should ground a very 
considerable presumption, that the one might replace the other 
in new and untried applications in Pharmacy. 

The illustration might be extended to Vegetable and to 
Animal species. A quadruped resembles a human being in 
very many points of structure and function, but also differi 
in a considerable number; while there may be undiscov 
properties in both. This reduces to a weak probability 
all inferences from one to the other as to the suitable kinds of 
food, liability to disease, or medical treatment. Experiments 
on animals may cast light on the human subject, provided we 
know that the particular organs are constructed nearly alike 
in both, as in the connexions of the nerves, the breathing, the 
digestion, &c The function of the saliva and of the gastric 
juice has been studied by experiments on dogs and on ho: 
In a recent set of experiments on the action of mercury, dogl 
were operated on ; care having been first taken to ascertain 
that they agree with human beings in the mercurial symptom 
of salivation. 

It is interesting to determine whether our inference from 
man to the lower animals as to the possession of conse 
ness, is an induction or only an analog}'. We believe that, in 
human beings, consciousness is always associated with a iri 
external manifestations, called the signs of feeling, and with 
an internal structure of brain, senses, and muscular 
This we hold to be an inductive uniformity complete 
lished as regards human beings. The inductio 
differences of degree; with fewer and feebler manifi 
and a smaller brain than usual, we couple a feel 
the mental functions. Now, the physical part is 
brutes ; some approximating more, and some 1 
the human type. It would seem, therefore, that by indue 
17 



376 ANALOGY. 

and not by analogy, we are to infer the existence of conscious- 
ness in the animals, with modifications of degree only. 

Mind and Body are of opposite nature ; they are the greatest 
of all contrasts. Yet there are points of analogy that have 
been made use of to furnish language and illustration from 
the one to the other. As in material phenomena, we may 
have a plurality of forces cod spiring or opposing each other, 
the resultant being arithmetically computable, so in mind we 
have motives uniting or opposing their strength, the effect 
being computable (although not with numerical exactness) by 
adding together those on each side, and noting which is the 
larger amount. Reid has objected to this comparison, re- 
marking that ' the analogy between a balance and a man 
deliberating, though one of the strongest that can be found 
between matter and mind, is too weak to support any argu- 
ment.' Yet, if the analogy is trusted only to the extent of the 
similarity, there is no good objection to making an inference 
from it. 'Now, the similarity is complete as far as regards the 
cumulative effect of concurring motives, and the neutralizing 
or frustrating effect of opposing motives. Whatever power a 
given motive adds to a man's volition when it concurs, it 
must subtract or withdraw when it opposes. 

The intrusion, by Aristotle and by Kant, of phraseology 
derived from the intellect, into the domain of the feelings and 
the will, may be pronounced an improper identification, or an 
abuse of analogy. Aristotle's syllogism of the 'Will, and 
Kant's categorical Imperative, point to no real resemblance ; 
a syllogism expresses an argument conducted by the reason- 
ing faculty ; it has no relevance or suitability to express the 
decisions of the will. 

Reflex Actions may be profitably compared with Voluntary 
Actions, if we confine ourselves to the points of similarity. 
The Reflex is the voluntary with consciousness suppressed or 
made unessential ; on the corporeal side, there is a consider- 
able amount of resemblance, or still better, a gradation or 
continuity. 

Until recently, the sun was considered to be only analogi- 
cally compared to terrestrial fires. The points of agreement, 
in giving forth radiant heat with light, are of the most essential 
kind ; but there was supposed to be a disparity also vital. It 
was conceived that the sun gave forth its vast flood of 
radiance, with no diminution of intensity. Now, every hot 
body on the earth cools by radiation. Until this serious dis- 
parity was got over, scientific men felt that all inferences from 



ANALOGICAL HTOOTHK81 

terrestrial bodies to the composition of the sun \ 
unauthorized. 

Much speculation has been expended on the qti 
the planets inhabited? The argument is ai 
and there is not even the force of anal 
ence to a small number. Bodies, like the mown, \ 
water and no atmosphere, must be dismissed al 
planets generally appear to possess atmosplu 

We seem justified, however, in making a summ; 
of the near and the remote planets, on the ground ol 
All organized life known to us, is possible only within na 
limits of temperature ; no animal or plant can exist eithi 
freezing -water or in boiling water. Now, the temperatui 
Mercury must in all likelihood be above the boiling } 
even at the poles, and the temperature of Uranus, ami of 
Saturn, below freezing at the equator. The constitnenl 
ments being now shown to be the same throughout the G 
system — Carbon, Oxygen, Hydrogen, &c, we are not to 
sume any such departure from our ow r n type of organized I. 
would be implied by animals and plants subsisting in I 
extremes of temperature. On the supposition that the e 
temperature has steadily decreased, and is still decr< 
radiation, the day of living beings is past for Uranus 
Saturn, and perhaps for Jupiter ; it is not begun lor Men 

Confining ourselves, therefore, to the neigh bouring plai 
and referring to the others only for the periods, past or future, 
when the capital circumstance of temperature is sui 
have an analogical argument as follows. Venus and Mai - 
gravitating masses like the earth, containing, we may no v. 
with certainty, the same materials as this globe — solid, 1 
and gaseous. But we cannot tell the precise arrangcmei 
the constituent substances ; and, seeing that with oui 
much depends upon the mere collocation and amount ot 
elements as oxygen and carbon, we may consider thi 
known properties of the supposed planets are c< 
number, and serious in character. The probability ai 
of the points of agreement, ifnot greatly affected by ki 
ferences, is reduced by this large element of the unki 

Many Hypotheses are of the nature of anal 
sons, the degree and value of the i 
less uncertain. Thus, to refer to the undi 
of Light. When Newton explained the v 
vibrations of the air in sound, by I 
lum, he was assimilating phenomena of the same m 



378 CREDIBILITY AND INCREDIBILITY. 

character, and reasoning only from the points of similar ity« 
But when we reason from the sonorous vibrations of the air 
to the vibrations of an ether assumed as occupying space, and 
conveying light and heat, we work by analogy. It would, 
therefore, not be irrelevant to apply the rule of analogy, and 
estimate the points of agreement, as compared with the points 
of disagreement, and conclude accordingly. On this view, 
the hypothesis would have but a small intrinsic probability ; 
it would be left in a great measure dependent on the kind of 
evidence already quoted in its favour, the tallying with the 
special facts of the operation of light. 

The first attempt to penetrate the mystery of nervous action 
was Hartley's hypothesis of vibratory propagation, based on 
the analogy of sound. The comparison was crude and un- 
satisfactory ; but there was a certain amount of likeness, and 
the inferences founded on that were admissible. It realized 
the fact of influence conveyed inwards from the nerves to the 
brain, and outwards from the brain to the muscles, thus 
suggesting a circle of action, which circumstance alone is 
pregnant with valuable conclusions, as appeared after the 
discovery of Bell gave new vigour to the conception. The 
vibratory mode of communication had no relevance, and any 
conclusions drawn from it were unsound. Next came the 
analogy to the electric current, which was much closer to the 
facts, more fertile in suggestions, and less charged with mis- 
leading circumstances. By taking liberties with current 
action, something like the liberties taken with the ether in 
adapting it for light, we are able to shape a view of nerve 
force that fits the actual phenomena with remarkable close- 
ness. A third mode of representing the action has been 
advanced by Mr. Herbert Spencer, which departs from electri- 
cal and chemical action and reposes upon the physical property 
called allotropism. 



CHAPTER XVI. 

CREDIBILITY AKD INCREDIBILITY. 

1. There are propositions supported by a certain amount 
of evidence, that are nevertheless disbelieved. From some 



CONSISTENCY WITH ESTABLISHED 

circumstance connected with them, they 
Incredible. 

Irrespective of the evidence specifically adduced in fai 
of a certain fact, we often pronounce it c ible ; 

in the one case we believe, and in the other disl 
the same amount of positive testimony. We 
slight report, that a fishing boat foundered in a 
we do not believe, without much stronger testimoi 
fully equipped man-of-war was wrecked. I 
rumoured that the Eddystone lighthouse was blown di 
every one felt that the rumour required confirmation. 

2. The circumstance that renders a fact Credibl 
Incredible is its being consistent or inconsistent with 
well-established inductions. 

In simple cases, this is apparent. That a child initiated in 
crime by its parents should become a criminal, is credible, 
cause it is highly probable, being the result of a well-gronn 
induction of the human mind. That such a child should turn 
out a paragon of virtue, as is sometimes described in romance, 
we pronounce improbable and therefore incredible, in the 
one case we are satisfied with a small amount of testimony, 
in the other case, we demand very strong evidence. 

We are thus often led to reject evidence at once on the 
score of antecedent improbability. We may be in the | 
tion of refusing a large amount of positive evidence ; 
a number of respectable witnesses testify that a man alter 
being immersed in the water for an hour has been resuscitated, 
It is to be remarked, however, that in all such cases the 
dence tendered is only probable ; it may have a very high 
degree of probability, it may be 500 to 1, yet it d 
amount to certainty. It fails once in five-hundred-and« 
times, and is therefore, in certain circumstances, i 
rejection. 

3. Such well-established scientific inductions, as the 
Law of Gravity and the Law of Causation, render w holly in- 
credible any assertion that contradicts them. 

That Mahomet's coffin hung suspended in 
\ table of its own accord mounted to the ceilin 
ire facts to be wholly disbelieved. 

All the alleged discoveries of a perpetual m 
ise of force out of nothing, are incredible ; 



380 CREDIBILITY AND INCREDIBILITY. 

to Causation as expressed under the Correlation or Persistence 
of Energy. All supposed modes of deriving motive power, 
otherwise than from solar heat past or present, are incredible, 
That any medium of force more economical than the combus- 
tion of coal remains to be discovered is all but incredible. 

If any one affirms that some change has happened without 
a cause, we refuse to listen to it. An exception to this rule is 
sometimes claimed in the case of the human will ; but that 
exception has never yet been established upon evidence suffi- 
cient to cope with the evidence in favour of the law of causa- 
tion. 

The principle laid down by Hume, that nothing is credible 
that contradicts experience, or is at variance with the laws of 
nature, is strictly applicable to these completely proved induc- 
tions. We cannot receive any counter evidence in their case, 
unless of a kind so strong as to reverse our former judgment 
and make them out to be mistakes. No mere probability is 
equal to this task in regard to the axioms of mathematics, the 
law of causation, the law of gravity, and many others. 

That every living thing proceeds from a previous living i 
thing, or as expressed by Harvey — omne vivum ex ovo, is an 
induction verified by simple agreement, through a very wide 
experience ; rendering spontaneous generation, for the present^ 
incredible. It is an empirical law, true within all the limits 
of human observation hitherto, although we may not be able 
to extend it over an indefinite period of time. 

Among facts antecedently incredible, we must rank the 
spontaneous combustion of a human being, which is totally 
inconsistent with the constitution of the animal body. 

It has been alleged by witnesses that the mummy corn of 
the Egyptian pyramids has been sown and been productive. 
To a botanist, the assertion is wholly incredible. Seeds two 
centuries old are so completely changed as to lose their 
fertility. 

There appears to be unexceptionable testimony to the prac- 
tice of the Indian Fakeers, in allowing themselves to be buried 
for a number of days, after which they are dug out alive. 
This would be wholly incredible, but for the knowledge that 
we have of such states as trance, or lowered animation, which 
dispense with food altogether for a time, and require only the 
minimum of oxygen. 

It is alleged by travellers that certain tribes subsist upon 
earth as food. This is admissible, only on the supposition 
that the earth contains a quantity of organic products, such 



COMPARISON OF PBOBABIUmfia 

as starchy sugar, albumen, or their equival any 

human being or animal could live upon tli 
matters of the soil is to be wholly disbelieved. 

The phenomena of clairvoyance are all in the po 
antecedent incredibility. That any one should 
eyes bandaged is at variance with the condi 
established by all the authentic experience of the hum • 
Yet this has been affirmed by multitudes of witn 
testimony of witnesses, however, in such a mat 
received. The sole condition of admitting such a fa 
be (what has never yet been attempted) a rigorous 
tion according to the methods of experimental Bciei 
with the other facts of the same class — prophetic di- 
visions or intimations of events at a distance. These arc all 
opposed to well-established inductions. 

4. When a fact with a certain amount of evid 

its favour, is opposed, not to an established induction, but 
to an approximate generalization or probability, t 
is one of computation of probabilities. 

"What is only probable, or approximately true, has 
tions ; an opposite assertion, therefore, may be credited, if 
supported by a still higher probability, or by a generalization 
approximating still more to certainty. A fact true nil] 
nine times in a hundred is not to be set aside by an oppi 
testimony correct only nine times in ten. 

In an age when physical laws were imperfectly un 
when the law of causation itself was not fully verified, 
phenomenon of witchcraft stood between opposing prob 
ties. There was no inductive certainty on the one b;w. 
controvert the mere probabilities of human testimony 
other. The physical knowledge even of Bacon 
enough to render the testimonies in support of * 
wholly incredible, although it might have stamp *»» 

inferior weight and cogency. 

5. The allegations of travellers as to l 
.plants, or of animals, are credible or in 

iug as they affirm what contradicts, or what does not 
tradict, laws of causation or of c< 

There are certain peculiarities of struct;. 
as cause and effect in the animal system 
must have an organ for receiving and digesting food, a 



3S2 CREDIBILITY AND INCREDIBILITY. 

tory organ, a means of reproduction. Any contradiction to 
these must be absolutely rejected. 

Next in point of evidentiary force are the typical peculiarities 
of the order, as the four limbs in the higher vertebrata. An 
animal of the higher tribes, with both wings and arms, would 
present an incredible combination ; there might not be absolute 
incompatibility, but there would be such a departure from the 
type as experienced, that it could not be received on less 
authority than ocular inspection fortified against every possi- 
bility of delusion. 

New combinations of compatible organs are improbable 
only in proportion as they have been hitherto undiscovered. 
Flying fish were improbable, but not to the degree of incredi- 
bility. The extension of our knowledge of kinds, by showing 
new variations, reduces the improbability in favour of other 
kinds, within the limits of compatibility. That a ruminant 
animal may be found without cloven hoofs is incredible, if 
these are cause and effect, or effects of a common cause , it is 
only improbable if they are co-existences without causation. 
Such a co-existence has been widely verified, but not as yet 
exhaustively. 

A late distinguished historian for a long time doubted the 
fact of persons having lived more than a hundred years. He 
did not regard the fact itself as absolutely incredible ; but in 
the absence of authentic registrations, and the uncertainty of 
memory and tradition extending to events a century old, he 
considered that the improbability of so great an age had not 
been overcome by sufficient counter probabilities. At length 
he obtained what he deemed adequate evidence in favour of 
centenarians. 

6. The assertion of a fact wholly beyond the reach of 
evidence, for or against, is to be held as untrue. 

We are not entitled to put the smallest stress upon a fact 
without evidence in its favour, because, from its being inacces- 
sible to observation, no evidence can be produced against it. 
To affirm that the centre of the earth is occupied by gold, is 
for all purposes, the same as a falsehood. 

On the Great Postulate of Experience, we are to believe 
that what has uniformly happened in the past will continue to 
happen in the future ; we accept uncontradicted experience as 
true. But where there has been no experience, we can 
believe nothing. We are not obliged to show that a thing is 
not ; the burden lies upon whoever maintains that the thing is. 



BOOK IV. 

DEFINITION. 

The processes having reference to the class, notion, or 
concept, have been already enumerated. The chief are. 

Classification, Abstraction, Naming (with a view to gener- 
ality), Definition. 

The class, notion, or concept as already explained, is a 
product of generalization. It may be constituted by one 
common property, as resisting, moving, white, bitter ; or by 
more than one, as house, mind, man. 

Classification, in its simplest form, follows the identifica- 
tion of like things ; that is, a class is made up of things brought 
together by likeness. When the mind attends more particu- 
larly to the points of community, it is said to put forth the 
power of Abstraction. A name applied to the class in virtue 
of the class likeness, is a General Name. The precise delinea- 
tion of the likeness by a verbal statement is Definition'. 

The three processes — Classification, General Naming, and 
Definition — are what we are now to consider. The first- 
named process, Classification, has a larger meaning than tne 
mere assemblage of things upon one or more points ot likei.- 
it includes the arts for systematically arranging vast multi- 
tudes of related objects, under higher and lower geneaa, as in 
what are called the three Kingdoms of Nature. With a view 
to this greater complication, we shall view the whole bo 
of Classification last of the three. 

As regards the generalization of the Class, or Not 
in all its aspects, the fundamental principle is 
follows : — 

Of the various groupings of resembling tlii 
ence is given to such as have in common the most iiuukt- 
ous and the most important attributes. 

This is the basis of natural or philosophical c! ions, 



CANONS OF DEFINITION. 

in contrast to insignificant and unsuggestive classifications; 
as in the distinction between the Natural and the Linnaean 
terns of Botany. It may be termed the golden rule of 
classifying. 

We are often disposed to prefer classes on acconnt of their 
extent, although the common attributes — the comprehension 
or connotation, may have dwindled down to a limited and 
unimportant resemblance. Thus, the class { land animals ' is 
very extensive, with little comprehension; and more insight 
is imparted by breaking it up into groups, as mammalia and 
birds, each having numerous and important points of com- 
munity. The class * adherents to a religious creed ' is so 
wide as to impart very little information respecting the indi- 
viduals ; the sub-classes Buddhists, Mahometans, Jews, Roman 
Catholics, Calvin ists, each connote a large circle of peculiari- 
ties. 



CHAPTER L 
CANONS OF DEFINITION. 

1. Definition consists in fixing by language the precise 
signification— the Connotation— of General Names. 

Defining does not apply to the unmeaning name. An arbi- 
trary name used for a particular object as * Sirius ' for a star, 
' Snowdon ' for a mountain, 4 Samson * for a locomotive, is ex- 
plained only by showing or indicating the thing.* 

Nevertheless, from the important consideration already 
stated (Introduction, p. 6), that even a singular is conceived 
by the mmd as a conflux of generals, Definition becomes 
eventually applicable to individual things. A particular star, 
a mountain, a locomotive engine, may be represented and 
winked off from all other things by a reries of descriptive 
names of general signification. For such an operation, how- 
ever the name Description is more appropriate. 

It has been already explained (Part I, p. 71) that a perfect 

Jetmition is the whole connotation of the name. Some notions 

nave one point of community; some two, three, or four ; some 

a great many, as the often-mentioned Kinds ; the proper and 

definUio'" £ 6 JE!&I !i hG ° l i 1 ?* icians ' <0m ™ int ^a notitia est 
attimtio - a mow of the thing itself is its best definition.' 



FUNDAMENTALS OF DEFINITION. 

complete Definition must give an account of them all. Tl.o 
singling out of one or two properties, for tbe mere purp 
discrimination, is not a proper or perfect definil 
s 2. From tbe very nature of human knowledge, Defini- 
tion appeals to the two fundamental principles 
and Difference, or Generality and Contrast 
I. Every generality must relate to particul* 
II To every real notion, as well as to every particular 
experience, there corresponds some opposil 
This is simply the Law of Eelativity or Contrast. 

As the statement of what is common to a number of j 
cular things, Definition is essentially a process of genen 
tion ; while neither particular things, nor their tents, 

have any distinct meaning, unless there be assignable a dis- 
tinct opposite. The act of Defining, therefore, con 
generalizing operation, rendered precise at every step in- 
explicit or implicit opposition, negation, or contrast. If', 
throughout the process of generalization, we avail our.- 
of explicit contrast, to render precise both the particular* 
the generalities, that one operation would be enough ; 
would be generalizing pure and simple, and nothing be- 
But there is often a great advantage gained by viewing, in a 
separate and distinct operation, the opposite or contrast of the 
thing defined ; and hence we may lay down two canons, or 
two stages of the process — the first the ennon of Generalfeai 
the second, the canon of Contrast or Relativity; or. as Gene- 
ralization must enter into both, we may call them the 
and Negative Methods. Taken together they show that 
Defining is rendered thorough-going, first, by generalizing the 
Particulars of the Motion 'propounded, and secondly, by 
generalizing the Particulars of its Negative. 

The method of Defining given in the ordinary works 
Syllogistic Logic contains no reference to a generali^ii 
tion. The scholastic definition direct* 
higher genus of the thing defined, and (2) the S] 
ence, or the distinction between the thin 
species of the same genus (j<er genus et < No 

mention is made of the way of obtaining either I 
of the genus, or the differential chars 

Suppose we were to define Chemistry in this way ; (genus) a 
Science, (differentia) having reference to a peculiar kind of 
Combination of Bodies, called chemical ;— it is obvious that 



CANONS OF DEFINITION. 

to give such a definition we must scan the subjects ordinarily 
included in Chemistry, and, by generalizing them, find aa 
expression suitable to them all, and to none besides. Hence, 
the direction to assign the genus and the difference, merely 
relates to the form of expressing the result of a generalizing 
operation. 

Allusion is made, by Mr. Mill, to a mode of defining by 
4 Analysis,' or by resolving a complex notion into its con- 
stituent elementary notions; as when we define Eloquence — 
1 the power of influencing men's conduct by means of speech. ' 
Here, Eloquence is a complex property, resolved into the two 
simpler properties, ' exerting influence over men's conduct,' , 
and l speech.' If, however, the enquiry was made, how do i 
we arrive at this definition, the only answer would be, by , 
generalizing from the particular examples of eloquent address ; , 
so that, in point of fact, this method, if it be a method, does 
not supersede the processes of generalization. 

The analytic statement could, if we please, be thrown into 
the scholastic form ; we have merely to adopt one of the com- 
ponent notions as a * genus,' and call the others ' differentia ;' 
influencing of men's conduct (genus), use of speech (differen- 
tia). ^ We might even reverse the notions ; ' speech' (genus), 
'for influencing human conduct ' (differentia). 

Thus, neither of these two modes of defining can come into 
competition with the main circumstance insisted on, namely, 
that to define is to generalize. On what occasions, the 
generalizing process may be dispensed with, will be a matter 
of future consideration. 

Positive Method. 

3. Canon. Assemble for comparison the Particulars 
coming under the Notion to be defined. 

By the Particulars are meant, not every individual instance, 
but representative instances sufficient to embrace the extreme 
varieties. 

To define a species of Plants, the botanist collects recognized 
examples of the species, including the widest extremes admitted 
into it. He compares the several specimens, noting their 
agreements, until he finds what characters pervade the whole ; 
these he expresses in suitable language, which language is 
henceforth the definition of the speoies. So, in dealing with 
the higher groupings— genera, orders, and classes— he follows 



GENERALIZATION OF POSITIVE rARTICUIAKS. 

tho same obvious plan. Likewise, the zoologist and mine. 
have, in the last resort, no other method. 

Farther to elucidate denning by the generalization 
the positive particulars, we will select examples bu 
bring out the difficult situations, and will indicate, in 
of subordinate canons, the modes of overcoming the difl 

Suppose we have to define a Monarch'/. Wo mu 
by assembling instances of every institution that baa 
been called by the name: the kings of the heroi 
Greece ; the Spartan kings ; the Roman kings ; the 
Macedonian, Syrian, and Egyptian kings; the Ten 
king; the kings of modern European nations; the kin 
the negro tribes; the emperors; the reigning dukes, mar- 
graves, counts, bishops, &c. To these we should have to add 
the king-archon at Athens, and the king of the sacrifice 
Rome — mere relics of the ancient kingly government (Sir 
G. C. Lewis, Methods of Politics, I. 80). Now, if we confined 
ourselves to a certain number of these, we should lind the 
common fact of absolute or despotic government; this, how- 
ever, fails to apply to other instances, as our modern constitu- 
tional monarchies ; and, if these are to be included, the 
common features are greatly reduced in significance, being, iu 
fact, little more than (1) the highest dignity in the state, and 
(2) a participation, greater or less, in the sovereign authority. 
But again, if we look to the two last instances — the k 
archon at Athens, and the king of the sacrifices at Rome- 
shall not be able to apply to them even the attenuated com- 
munity just given ; there would be required a still farther 
attenuation, reducing the points of agreement to utter insigni- 
cance. 

Now this is one of the most usual situations arising in 
the attempt to generalize a notion with a view to denui 
We must be led in the first instance, by the popular denota- 
tion of the name ; yet, if we abide by that, we fail to ol 
any important community of meaning. It is in such a per- 
plexity, that the golden rule must be called to our aid ; we 
must take some means to form a class upon a deep and wide 
agreement. If need be, we must depart from the 
tatioii; leaving out some instances, and taking in otfa 
we form a class really possessing important class attrib 
Thus, in the case of the monarch, we should cut off at 
the mere relics of old kingly power. As regards th< 
should divide the instances between the b 
limited monarchies ; there is a large and important community 



CANONS OF DEFINITION. 

of meaning in the class termed * absolute monarchies/ and 
this class should be isolated, and should make a distinct notion 
in political science. The remaining individuals should be dealt 
with apart; they (as shown by Sir G. C. Lewis) are far 
better excluded from Monarchies, and classed with Republics. 
'1>V including in monarchies, and excluding from republics, 
every government of which a king is the head, we make every 
true general proposition respecting monarchies and republics 
impossible.' In this state of things an operation of re-classing 
is the indispensable scientific corrective of the popular and 
received generalities. 

The definition of a Colomj would afford a case exactly 
parallel. Taking together all the things that have ever borne 
this name in ancient or in modern times — the colonies of the 
Phenicians, Greeks, Romans, Italians, Spaniards, Portugese, 
Dutch, French, English — we should find these facts in common, 
namely, emigrating from the mother country, settling in some 
new spot, and displacing the previous government, if not also 
the population, of the place occupied. With this small amount 
of agreement, there are very wide disparities , and until we 
narrow the. instances, we do not arrive at a large and im- 
portant connotation or meaning. If, however, discarding the 
ancient colonies, we make the comparison among the modern 
instances, we find the important circumstance of a sustained 
political relationship with the mother country ; which is 
better expressed by the word dependency . And by sub-divid- 
ing the class, we can obtain inferior classes, with still more 
numerous important points of agreement ; as, for example, 
the Canadian and Australian colonies of this country, which 
exercise the powers of independent legislation, under the 
least possible control by the home government. 

Let us next endeavour to define Food. According to the 
canon, we assemble representative examples of all the sub- 
stances ever recognized under this name. We have before us, 
the flesh of animals, the esculent roots, fruits, leaves, &c. 
We have also a number of substances of purely mineral origin, 
as water and common salt. Our work lies in generalizing 
these, in detecting community in the midst of much difference. 
Were man a purely carnivorous feeder, his food might be 
generalized as the flesh of animals taken into the mouth, and 
passed into the stomach, to be there digested and thence to 
be applied to the nutrition and support of the system. But 
when we include vegetable and mineral bodies, we must leave 
out 4 flesh,' and substitute 'animal, vegetable, and mineral 



RULE OF IMPORTANT COMMUNITY. 

substances ;' the other part of the stitemeni being applic 
Even as amended, however, the definition is si ill tentative, 
needs to be verified by comparison in detail with everything 
that has ever been put forward as food. We must chall 
all informed critics to say where the definition fails. i 
nourishment is afforded by substances absorbed through the 
skin, which would exclude the medium of the mouth 
Btomach, and narrow the definition to nourishing orsuppoi 
the system. Again, it is doubted, whether alcohol, 
tobacco (chewed) really nourish the system. This is a far 
more serious objection; and the manner of dealing with it 
will illustrate the principles of defining. 

In the first place, there may be a contest as to the matter of 
fact. Could it bo shown that these substances do give nourish- 
ment, support, or strength to the system, the difficulty is at 
once overcome; in that case, they fall under the definition. 
On the contrary supposition — that they do not nourish the 
the system, — two courses are open. First, we may exclude 
them from the class * Food,' and retain the definition. Or 
secondly, we may include them, and alter the definition. As 
modified to suit the extension, the definition would be ' sub- 
stances that either nourish or stimulate the system.' To de- 
cide between those two courses, we must, as before, refer 
to the golden rule of classification, which recommends the 
adherence to a smaller class founded on a great and important 
community, rather than to a larger where the community of 
meaning is attenuated to comparative insignificance. Better, 
therefore, to retain two groups — Foods and Stimulants, — 
each with its own definition. In that way, we should derive 
much more information respecting any individual thing de- 
signated either 'Food' or ' Stimulant/ than if the word 'food 1 
covered both. It may be that some substances combine both. 
functions; which would entitle them to be named in both 
classes. 

We may notice the definition formerly given of ' 
by way of remarking that a definition is obviously 
that does not distinguish the given notion from 
already settled. Thus, unless an Axiom be a real 
tion, it is not divided from Definitions; and nnless 
fundamental within the science, it does not difter I 
body of Propositions so far as employed to proi 
positions. The characters proposed are a 
constitute a separate notion bearing the name. 

These cases sufficiently exemplify the situation whero a 



390 



CANONS OF DEFINITION. 



-word is extended to denote things that have few or no im- 
portant points of community. The next example will bring to 
view a perplexity of another kind. 

Suppose we seek to define a Solid. Summoning to view, if 
not all the solids in nature, sufficient representatives of all the 
varieties compatible with the name — metals, rocks, woods, 
bones, and all the products of vegetable and animal life 
denominated solid — we set to work to compare them, and 
note their agreement. There is little apparent difficulty in 
this instance. We see that, however various these bodies 
may be, they agree in resisting force applied to change their 
form ; so readily does this strike us at first sight, that the case 
seems searcely worth producing to exemplify a logical formula. 
Let us, however, apply the Socratic test — exposing the defini- 
tion to the cavil of every objector, — and we shall probably 
soon be told of a grave difficulty. The quality, so very 
decided in the great mass of instances, is found to have 
degrees, to shade insensibly into the state called 'liquid/ 
where solidity terminates. Now, at what point does solidity 
end, and the opposite state begin ? Is a paste, a glue, a jelly, 
solid or not ? Is Hamlet right in talking of ; this too, too 
solid flesh f 

We have here not a mere cavil, but a frequent and serious per- i 
plexity. Many couples of qualities, unmistakeably contrasted in 
'the greater number of instances of them, pass into one another 
by insensible gradations, rendering impossible the drawing of 
a hard and fast line. Who shall say at what moment day ends' 
and night begins ? So, there has always been a doubt as to 
the exact individual that ends the animal series, and is neigh- 
bour to the beginning of the plant series. Sleeping and 
waking may have an intermediate state, with difficulty as- 
signed to either. The great chemical sub-division into metals 
and non-metals has an ambiguous border in the substances 
arsenic and tellurium. In the animal system, the voluntary 
shades insensibly into the involuntary. 

The Greek philosophers displayed to the utmost the in- 
genuity that lights upon difficulties ; and this example did not 
escape them. They grounded upon it a puzzle named the 
Sorites, or heap. A certain heap was presented, which was 
fairly designated small ; it was then increased by very gradual 
additions; and the spectator was challenged to declare at 
what point it ceased to be small, and deserved to be accounted 
large. 

There is but one solution of the riddle. A certain margin 



MARGIN OF TRANSITION. 

must be allowed as indeter mined, and as open to difl 
opinion ; and such a margin of ambiguity id 
invalidating the radical contrast of qualitu 
No one would enter into a dispute as to the i 
day passed into night; nor would the uncertainty a 
moment be admitted as a reason lor confounding day 
night. We must agree to differ upou the instants o 
tion in all such cases. While the great body of the non-m 
can be distinctly marked off from the metals, we refrain 
positively maintaining arsenic and tellurium to he of ei 
class ; they are transition individuals, the ' frontier ' i 
of Bacon ; in that position we leave them. 

There is a margin of transition in the ethical distinction i f 
Reward and Punishment. In the great part of their exl 
these two motives are amply contrasted ; to bestow a reward 
for performance, is a different thing from inflicting punish- 
ment for non-performance ; and the withholding of a re 
is not confounded with punishment. Yet circumstances arise 
when the one merges into the other. A kind parent with* 
holds from a child some indulgence originally meant as a 
reward ; if the indulgence has been so frequent as to become 
a kind of use and wont, the privation is hardly distinguishable 
from punishment. 

When it is said, no man is to be punished for his opinions, 
we are not to infer that each person is bound to asso 
alike with all persons of all opinions, because to give a prefer- 
ence is to stigmatize some at the expense of others. Our not 
choosing any one as a companion and friend is not to be held 
as inflicting a penalty, or as manifesting disapprobation. 

We may farther exemplify the method upon Mutter. As- 
sembling the various things recognized as material, say solid 
and liquid bodies, and comparing them among themselves, we 
find a unanimity in these points, namely, resistance to m >tion 
or force applied' to them, and exercising power or force when 
in motion. All solids and all liquids agree in these 
They farther agree in being visible and tangible. Y\ i 
next bring into comparison the gaseous bodies I>> I 
possess the same quality as to resistance and moving 
The identity is not at first sight apparent, but I 
a closer inspection; airs resist motion, and c 
power, although in a comparatively less degree th 
and liquids. They are not, however, as a 
tangible; consequently, either these qualiti 
or gaseous bodies must be excluded; wo must make our 



392 CANONS OF DEFINITION. 

choice. The decision is not difficult. So exceedingly import- 
ant is the material property of Resistance and Momentum 
("•iven in one word — Inertia), that we are justified in making 
it the foundation of a class, even although we associate 
together t Kings visible and tangible, and things invisible and 
intangible. 

The next enquiry relates to the Echer, or etherial medium, 
occupying all space. Shall this be included in the class 
4 Matter ? ' If the property of Inertness can be proved to 
belong to the supposed Ether, we must include it. On the 
contrary supposition, we are in the alternative position already 
exemplified ; we must either exclude the instance or attenuate 
the defining properties. Now, the only community that 
could exist between an unresisting Ether and Matter would 
be this very general circumstance, namely, being an extended 
medium for the operation of forces. The supposed ether con- 
veys light and heat, and is therefore a transitory embodiment 
of molecular force, as solids, liquids, and gases, are of force, 
both molar and molecular. Better, however, on this extreme 
supposition, not to class the Ether with Matter, but to leave, 
as the defining propsrty of Matter, the all-important fact des- 
cribed by Inertia. 

The foregoing instances under the Positive Canon are 
enough to show Definition in its primary character as a general- 
izing operation, and also to bring out the leading difficulties of 
the process— the adjustment of the particulars to comply with 
the golden precept, and the allowance of a doubtful margin in 
cases where opposites pass insensibly into each other. 

Negative Method. 

4. Canon. — Assemble for comparison the particulars of 
the Opposed, or contrasting Notion. 

This amounts to saying that, with the given Notion, we 
sshaltalso define, by the same generalizing method, the oppos- 
ing Notion. As it is impossible for anything to be precisely 
defined, unless its opposite is known, and defined with equal 
precision, we must in substance perform the two-fold opera- 
tion, whether or not we formally separate the opposing aspects. 
The cases where the formal separation is expedient will be 
made manifest by a few examples. 

It is impossible to place the human mind in a more favour- 
able position for comprehending a generality, than by laying 



CONTRAST. 

out to the view two arrays of particulars— the one red- 
ing the given notion, the other its negatn 
Straightness, for example, is thoroughly Bet forth bj 
a series of straight objects (of all varieties in other pi 
side by side with a series of bent, curved, or crooked oh 
Supposing the representation of both sides fco be com 
very utmost has been done to put the learner in poa 
the notion, idea, or concept, called 'straight. 1 

Let us apply the method to the definition of a Soli 
positive generalization leads to the expression of the 
attribute thus : — 'Solids resist force applied to elm 
form.' Try next the negative plan, by generalizing liquids 
(and gases). On an adequate comparison of these non-solids, 
we are able to say, 'liquids and gases yield to the slightest 
pressure, and have no fixed form, except as given by solid 
enclosures;' which is the exact obverse, and, therefore, the 
confirmation of the prior statement with reference to solids. 

Reverting now to the definition of Matter, already worked 
out on the positive side, let us seek for a negative generaliza- 
tion. But what is the negative of Matter? Most per 
would answer ' Mind ; ' which is true, but not the whole truth. 
Matter is indeed opposed to Mind ; but it is also opposed to 
Space unoccupied (except by the supposed Ether). The com- 
plete opposition to Mind is Extension, whether as resisting 
Matter or unresisting Space. We have therefore to oppose 
Matter to Space^ and ask the definition of Space. Now, on 
comparing all our experiences of what we term empty or un- 
occupied space, we find this common fact, freedom to mot \ <>r 
scope for movement; a definition the exact obverse of the 
definition of matter, or of the fact called Resistance or Inert- 
ness. 

Matter is sometimes opposed to Force. An argument for 
the immateriality of mind is founded on this opposition. 
Thus Hartley says, matter which is inert, cannot be the 
stance of mind, which is active, or a source of power. This 
is a pure mistake and confusion of ideas. It I 
aspect of Matter— resistance, and drops the other 
moving force. The two aspects are inseparable; 
moving matter; without matter there is no for 

The method of Opposires will be seen to adva 
fining Chemical Combination, the subject matter i 
of Chemistry. By the positive canon, we have 
numerous instances of the so-called Chemical 
union of oxygen and hydrogen to form water, oxy 



391 CANONS OF DEFINITION. 

carbon in carbonic acid, &c. The operation would turn out a 
very laborious one, from the great multitude of the particulars 
to be examined even for adequacy of representation. Wo 
shall, however, suppose that there has been obtained a general 
Statement of the points of community; namely, change of 
properties, definite proportions, and heat. 

We next ask what is Chemical Combination opposed to ? 
Of the genus — Combination, what are the species not chemical ? 
The answer is Mechanical mixture and Solution (in its broad 
phase of molecular adhesion). We should then have to gene- 
ralize these two, and confront the points of agreement with 
those above given. Now, we may dispense with drawing a 
formal contrast between Chemical union and Mechanical 
mixture ; for this reason, that the two are so prominently 
distinct as not to be in danger of being confounded. The 
profitable contrast is with Solution. Generalizing the instances 
of solvent attraction — in common solutions, in alloys, &c, — 
we see that although the solidity of a body may be broken 
up, or its state changed, it retains the greater number of its 
characteristic properties ; salt and sugar, when dissolved, are 
the same for most purposes ; the change is comparatively 
insignificant. Again, solution may be in all degrees up to 
saturation. Finally, solution is usually a cooling operation. 
These are the precise opposites of Chemical union. We may 
draw up a pointedly contrasting definition in this form : — 
Combination Solution 

Characters of the Compounds 
Merged Retained 

Proportion of Combining 
Definite Indefinite 

Eesulting change of Temperature 
Heat Cold. 

In the above instance, the Negative generalization is the 
easier of the two ; the field of instances being sooner over- 
taken. The same advantage belongs to the defining of Mind 
by the opposite. The particulars constituting Mind are 
numerous, various, and complicated ; the particulars consti- 
tuting Extension, the property opposed to mind, are much 
sooner gathered up into a general notion, and that notion is 
much more distinct and familiar than the properties of mind : 
moreover, the community of Extension is single ; of mind, 
plural. 

Opposing notions, having between them a border of ambigu- 
ous instances, are best cleared up by the methed of Negation, 



COMPLEX NOTIONS, 






I, with pointed contrast. We formerly had to notice I 1 i 
i; of the line that, on some occasions, dn 
J the Proposition; the definition of a complex notion 
i often very difficult to distinguish from n Proposition. 
Appetite is not sufficiently defined unless p >intedlv 
: to the notion most nearly allied with it— Desire. 

The principle of Utility, as the moral standard, Is opposed by 
Bentham, to the two principles— Asceticism, and £ 
or Antipathy (Sentiment). 

The Plant or Vegetable is defined by a parallel array of 
contrasts with the Animal ; and conversely. 

Deductive Definitions. 
5. When Complex Notions are formed by cornpotmd- 
• ing simpler notions, as in the Deductive Sciences, they 
> may be defined by stating their composition. 

In the Deductive Sciences, as Mathematics, notions as well 
as propositions are formed by artificial composition or deduc- 
tion. Given the notion 'triangle,' and the various notions 
'right angle/ 'equality,' &c, we can construct tlu complex 
notions 'right-angled triangle,' equilateral triangle,' ' isosceles 
triangle.' Xo reference to particulars is needed for defining 
such notions ; we merely recite the elements used in com- 
pounding them ; 'aright-angled triangle is a triangle with 
one right angle.' 

Having the notion ' attractive force,' and the various numeri- 
cal notions, squares,* cubes, &c, we constitute the artifi 
compounds, ' force as the square of the distance, the cube of 
the distance,' and so on. 

This is the one grand exception to the principle of defining 
by the generalization of Particulars. From the magnitude of 
our Deductive Sciences, there is a very large number of such 
notions ; and they have been the means of withdrawing atten- 
tion from the fundamental process of Defining through the 
comparison of instances in the concrete. 

We make artificial compounds, not merely for B 
ends, as in the Deductive Sciences, but also in th 
Imagination, as when we feign gods, demi-gods, dem 
gons, and ideal personages and scenes in po< 
tion of these notions also is the statement of their con. 

The Language of Definii 
6. The Language of Definition consists in assigni 
constituents of a Complex Notion. 



396 CANONS OF DEFINITION. 

The dictionary definitions by synonyms have an inci- 
dental value, but are not proper definitions. 

The generalizing operation terminates in the seizing of com- 
mon features, which have to be embodied in language. Now, 
the language used must express some more elementary notions, 
whose combination gives the required notion. 4 A solid resists 
force applied to change its form ' — is an expression substitu- 
ting for the word * solid ' a coalition of more elementary and 
general names — ' resistance/ ' force,' ' change,' * form.' The 
definition of Property is — c the right of each person to dispose 
of whatever things of value they have either acquired by their 
own labour, or obtained by free gift or by fair agreement from 
those that have so acquired it.' Here the constituent notions 
are* right,' 'disposal,' 'value,' 'acquisition,' 'labour,' 'gift,' 
4 agreement.' 

Liberty is definable as the power of using one's faculties at 
will, subject (if Civil Liberty be meant) to not interfering 
with the like use in others ; implicating ' power,' ' faculties/ 
1 will.' 

Thus the so-called method of * Analysis ' is the method of 
expressing every proper Definition. Whether the source of 
the definition be the generalization of particulars, or whether 
it be deductive as just explained, the wording of it is analytic. 

The use of synonyms in defining depends upon the circum- 
stance that almost every notion or thing has a plurality of 
names, and may be better known by some of these than by 
others^ There are many names for the fact called ' pleasure •/ 
joy, enjoyment, delight, happiness, felicity, delectation, rapture, 
ecstacy. The less familiar of these names are explained by 
the help of the more familiar ; but this is not scientific defining. 

7. The scholastic formula of defining — per genus et 
differentiam— -like Analysis, belongs to the expression, 
rather than to the discovery of the 'meaning of a notion. 

Each of the constituent notions expressing a complex notion 
is necessarily more general than the compound. 'Three,' 
| side/ and ' figure ' are each more general than the notion 
'triangle,' which they express by their combination. We 
ma}-, therefore, take any one of these and call it generic or the 
genu— say ^ figure : ' ' triangle ' is then a species of figure ; and 
its differentia or specific marks discriminating it from other 
figures are given in the remaining characters ' three ' and 
side, combined into 'three-sided.' So, if eloquence be 



GENUS AND DIFFERENCE 

defined, analytically, as ' the influencing of mon'i 
conduct by means of speech,' we might call ' in 
men's conduct,' the genus, and 'the employment of 
the specific difference. Wo might, also, invert the I 
and make 'speech 7 the genus, and 'influencing i 
difference. 

This latitude, however, is usually restrained by the circum- 
stance that one of the constituent properties Is the basis of a 
recognized class, already existing. Tims, in defining 
'line' is the recognized genus, and 'equal distance from a 
point,' the specifying attribute. A great number of cl 
and class notions fall under some superior class, or notion, on 
some one or more of their attributes. Not to mention the 
systematic classifications of Natural History, we may point to 
such cases as Painting (genus Fine Art), Mathematics (genus 
Science), Prudence (genus Virtue), Planet (genus Heavenly 
Body), Gold (genus Metal), Whiteness (genus Colour), 
Cathedral (genus Building). 

Instead of presenting an exhaustive analysis of a notion, or 
class connotation, this method supposes that generic prope 
are already known, that people are, as it were, educated up 
to the point of comprehending the genus, and need only to 
have the genus mentioned, and the specific differences stated. 
Thus Mathematics is the Science (genus) of quantity (differ- 
ence). Ethics is the Science (genus) of men's duties (differ- 
ence). Painting is the Fine Art (genus) that works by colour 
(difference). Poetry is a Fine Art employing the instrument 
of language. Prudence is a Virtue (genus) having reference 
to the welfare of the individual agent (difference). Justice is 
a Virtue, involving an equal and impartial distribution of ad- 
vantages, according to a received scale or standard. Polite- 
ness is Benevolence in trifles. Religion is Government 
(genus) by a Supernatural power (difference). Wonder, Fear, 
Love, Anger, are of the genus 'Emotion,' each havii 
specific difference. Sight is of the genus ' Sensation ; ' 
ference, ' by the Eye.' 

Locke's remarks on the scholastic type are very much in | 
They are in substance these :— When, in defining, we m 
the genus, or next general word, it is not out of 
only to save the labour of enumerating the e 
that such general word already expn 
of not being able to give the full enumeration). D< nml 
nothing but making any one understand by words wh 
given word stands for, it is best made by giving all t 
ideas combined in the signification of the term; audit p 



39S CANONS OF DEFINITION. 

have been accustomed, instead of the full enumeration, to use the 
next general term, it is neither from necessity nor for greater clear- 
ness, but for quickness and despatch. (Essay. Book III. Chap. II.) 

Ultimate Notions. 

8. For simple or Ultimate Notions, the generalization 
from Particulars still holds, but verbal expression neces- 
sarily fails. 

For attaining the notion * whiteness ' we gather particular 
examples of white colour, and of colours not-white. The 
conjunct impression of the positive and the negative particu- 
lars does everything that can be done to master or to convey 
the notion ; we may then attach a name to enable it to be 
spoken upon, but we cannot give a verbal definition of it; 
there are no notions, more elementary, whose combination 
would give the notion * white.' So we cannot by any form of J 
words convey the idea of i resisting ; * as an ultimate fact it 
can be known only in the actual experience of a comparison 
of resisting things. 

We may define Equality by Coincidence, but we can give 
no definition of Coincidence, we must show it. Any attempt 
at verbal expression, by such synomyms as ' agreeing in size/ 
' exactly fitting,' would be illusory. 

Succession and Co-existence are an ultimate contrasted 
couple, definable only by reference to examples. 

Unity and its opposite, Plurality, are indefinable. Wo 
must produce an array of objects with the common attribute, 
singleness, and another array of groups, and the comparison 
of the two arrays by the observer is the only possible mode of 
attaining the conception. 

A Mathematical point is indefinable. The definition given 
in books in geometry, « position without magnitude ' is not 
more elementary but more complex, than the thing defined. 
The correct mode of defining a point for geometrical purposes 
seems to be to indicate to the eye positions or landmarks 
where we begin or end a measurement, or make a division. 
The knowledge of a point or a position is obtained in the same 
concrete examination that gives length and space dimensions. 

A line is not definable ; as just noticed, it is an abstraction 
derived frorn comparing extended bodies. 

An angle is not definable ; ' inclination ' is merely another 
name for the entire notion, it is not a simpler or more elemen- 
tary conception. Actual examples must be shown. There is 
a mutual implication of a circle with an angle, so that if we 



INDEFINABLE NOTIONS. 

were made to master a circle in the first instance, wo D 

then learn an angle by definition ; but in the pn 

ing the circle we conld not avoid knowing an angle. # 

* Complex ideas,' says Hume, « may, perhaps be well known by 
definition, which is nothing but an enumeration of those pai 

* Our sensibilities in general give us the experiences of Dill 
Agreement; Quantity, amount or degree , Number, or discrete qu 
and Time (Succession is not fully given until we have th 
ence of the simultaneous, an acquired and complex notion). 

The Muscular sensibilities, in particular, give Resistance and Motii D ; 
which, by the farther help of sense expeiiences, arc unfolded into 6 
and Co-existence: 

Every one of the Senses contains one or more ultimate experiences ; no 
one sense can enable us to conceive what belongs to another. What 
number of independent or underivable sensations should be attributi d to 
each sense, we cannot easily sav ; whiteness, and the simple colours must 
be conceived as ultimate; while even the compounds and shade 
colour are probably for the most part beyond our power to conceive by 
any mere constructive effort, or apart from actual experience , a circum- 
stance that would make the ultimate notions of eight very numej 
Similar remarks may be extended to Sounds, Touches, 'Smells, and 
Tastes; under every one of these classes of sensations, there must 
considerable number that cannot be referred by derivation to others, and 
must be separately experienced. Our Organic Sensibilities, in like man- 
ner, contain numerous characteristic and independent modes ; hunger, 
thirst, repletion, suffocation, headache, rheumatism, &c, are all indefin- 
able by analysis, because they are ultimate modes of sensibility. Even 
although many of them have a common character, pain, they have a 
speciality which can be understood only by being felt. 

In the higher Emotions, as Wonder, Fear, Love, Anger, Pride, 
Curiosity, we have many compound states. The aesthetic pleasures 
combination of simpler modes. Still, a certain number of emotions are 
to appearance ultimate, as Wonder, Fear, Tenderness, Power ; while 
there is an absolute certainty that they could not be conceived without 
being actually felt. Moreover, many emotions that the Psychoid 
able to analyze could yet be constructed only with very great difficulty by 
the help of the elements alone. A person that never experienced the 
sentiment of veneration could scarcely arrive at it by merely being told 
what are its constituents. 

The elementary experiences of the mind are, therefore, very numi 
and so, therefore, are the indefinable notions. The varied situ,;' 
of human life give birth to notions practically indefinable ; 
of a Political Society could not be communicated to any one 
never been a member of some actual society. Hence, in our attempt! to 
define Government, Law, Authority, we must make an appeal to tie 
crete experiences of the listener. 

When all such cases are taken into account, the no! ions tint 
indefinable and ultimate nature must be reckoned by hundi 
ary makers have hitherto overlooked this circumstance ; and hi DOC th- ir 
pretended definitions revolve in a circle of words, where I 
a reference to actual things. How vain is a verbal definition oi 
words as light, heat, motion, large, up, fragrance, pain, wonder ! 
18 



400 CANONS OF DEFINITION. 

simple ideas, that compose them. But when we have pushed up 
definitions to the most simple ideas, and find still some ambiguity 
and obscurity ; what resource are we then possessed of ? By what 
invention can we throw light upon these ideas, and render them 
altogether precise and determinate to our intellectual view ? Pro- n 
duce'the impressions or original sentiments, from which the ideas 
are copied.' 

Locke considers himself to have been the first to remark that Sim pie 
Ideas are indefinable. By Eeid and by Stewart, the merit of first 
stating the fact is ascribed to Descartes. Hamilton would trace 
it back to Aristotle (Reid's Works, p. 220) : but Mr. Mansel 
questions the interpretation put by Hamilton upon the passage 
apparently relied on (Aldrich, Appendix, Definition), and quotes a 
remarkable passage from Occam, approaching closely to Locke's 
position concerning Simple Ideas. Aristotle, says Mansel, may be 
cited as an authority for limiting the indefinable to Summa Genera 
and to Individuals. 

Aristotle's general theory of Definition is much perplexed by \ 
being treated as an investigation of Cause, and by keeping up the 
distinction of Substance and Attribute. But, in regard to ' hunt- 
ing for,' as he expressed the search after, a definition, he allows 
the method of generalization from particulars, as well as the deduc- 
tive method, by working down from a higher genus. He also 
gives an intelligible distinction between Nominal and Heal Defin- 
ing. The Nominal definition applies * where there is no evidence 
of the existence of the objects,' as when we define a purely ima- 
ginary being, such as a centaur. This of course could only be a 
deductive definition. Beal definition applies to things known to 
exist and would be most completely exemplified in defining by a 
generalization of particulars. 

Mr. Mill draws the line between Nominal and Real Definitions 
— Definitions of Names and Definitions of Things — by remarking 
that the last-named kind, along with the meaning of a term, 
covertly asserts a matter of fact. (Book I., Chap. VIII.). The 
Eeal Definition postulates the real existence of the thing defined. 
In another place, however (Book III., Chap. V.), while discussing 
the hypothetical character of the Definitions of Geometry, Mr. 
Mill remarks truly that in order to reason out facts we must shape 
oi:r hypotheses to facts ; imaginary assumptions could bear 
imaginary consequences, but we need real assumptions in order to 
give real consequencea 



CHAPTER II. 

GENEEAL NAMES. 

1. General Names may not be absolutely indispensabla 
to general notions, but, besides being necessary to cora- 
munication, they aid the memory in remembering 
lities, while without them, we could not combine a number 
of distinct notions into propositions and reasonings. 

We might discover similarities in nature, and might remem- 
ber and act upon such discoveries, without the use of language. 
We could not, however, impart such discoveries to others. 
We might, indeed, in some instances, put the resembling 
things side by side, which would make tbe identifying opera- 
tion somewhat easier to those that came alter us. 1 
similar device, we might indicate a natural conjunction, in 
certain very limited circumstances. Tbe powers of fire might 
be expressed by putting on one side of a fire, a pile of wood, and 
on the other a heap of ashes; even this would not be intelligible 
without pantomime. But beyond the simplest cases, tbe 
attempt at expressing general laws would utterly break down. 
Our own recollection of discoveries of identity is vastly 
lightened by the use of names. Tbe employment of the same 
name to the resembling things, both expresses tbe thing 
individuals and declares their community or likeness; this 
mode of signifying likeness being of all others tbe least bur- 
densome to the memory. The complex and many-sided like- 
ness in difference, characteristic of natural objects — tbe 
possibility of including the same object, an orange for exam- 
ple, in a great number of classes — renders this easy mo 
keeping the various communities before tbe mind, of ii 
mable value. By the use of a few terms— round, yellow, 
sweet, we can compendiously grasp all tbe relation.-! 
orange, and make them enter into our reasonings with i 
parative ease. No discovery of identity ami 
secured against neglect, until, joined to a common 
can be borne in men's minds by means of thi 
constant insinuation. 

2. The conditions of general Naming fall under two 
heads. 



402 GENERAL NAMES. 

First. Every name should have a meaning well defined. 

The necessity of this is too obvious to need enforcement. 
Every science should have all its terms defined. The end of 
the Logic of Definition is to ftx the meanings of general names. 

We find in point of fact that words often possess numerous, 
distracting, and incompatible meanings. Take the familiar 
term ' stone.' It is applied to mineral and rocky materials, 
to the kernels of fruit, to the accumulations in the gall bladder, 
and in the kidney ; while it is refused to polished minerals 
(called gems), to rocks that have the cleavage suited for roof- 
ing (slates), and to baked clay (bricks). It occurs in the de- 
signation of the magnetic oxide of iron (loadstone), and not 
in speaking of other metallic ores. Such a term is wholly 
unfit for accurate reasoning, unless hedged round on every 
occasion by other phrases ; as building stone, precious stone, 
gall stone, &c. Moreover, the methods of definition are 
baffled for want of sufficient community to ground upon. 
There is no quality uniformly present in the cases where it 
is applied, and uniformly absent where it is not applied ; 
hence, the definer would have to employ largely the licence 
of striking off existing applications and taking in new ones. 

3. The demand for new names is a cause of the loose 
extension of words already in use. The processes of ex- 
tension are Similarity, Composition, and Contiguity. 

(1) The operation by Similarity is described by the name. 
A new object is brought into comparison with some one 
already known, and the name transferred accordingly. Thus, 
on the discovery of an additional coal-field, all the designations 
previously in use in connexion with coal are legitimately ex- 
tended to the new formation. More precarious extensions by 
similarity are often made. It is enough to mention the whole 
class of metaphors, wherein, by virtue of similarity, accom- 
panied by serious diversities, old words are employed in new 
meanings — < light ' to signify knowledge, •fire' to denote 
zeal and irascibility, c birth ' and ' death ' to mean many things 
differing widely from the beginning and the ending of life in 
an organized being. 

(2) The process of Composition is shown in framing new 
words, by the union of existing words ; as log-book, mince- 
meat, hail- stones, far-sighted, and by the systematic employ- 
ment of prefixes and sufilxes, prejudge, undo, withhold, 
boundless, wisdom, bearer, unnecessary. 



TRANSITIVE MEANINGS OF NAMES. 

The same process is seen in using a plurality of \ 
convey a single meaning : as in the systematic designation bj 
genus and species, white man, moss rose; and in numi 
many-worded combinations aud circumlocutions — 'the 
surviving descendant of an ancient family,' 'the fathei 
History.' 

(3) The process of Contiguity is exemplified in the G 
called Metonymy — as in using the 'crown' for royalty, 
'turf for horse-racing. So long as the figurative char 
of this operation is kept in view, there is no harm done, 
more dangerous employment of contiguity is exemplified m 
what is termed the 'Transitive application of words.' 
operation demands special notice. 

4. A word originally applied to a thing, by virtue of 
quality, may contract the additional meaning of sum.; 
associated quality, and thence be extended to things pos- 
sessing the second quality singly. 

This tendency was brought into prominence by Du 
Stewart, who gives the following symbolical elucidation of it. 
' Suppose that the letters A, B, C, D, E, denote a series of 
objects ; that A possesses some one quality in common with 
B; B a quality in common with C ; C a quality in common 
with D ; D a quality in common with E ; while at the same 
time, no quality can be found which belongs in common to 
any three objects in the series. Is it not conceivable, that the 
affinity between A and B may produce a transference of the 
name of the first to the second ; and that, in consequence of 
the other affinities which connect the remaining objects to- 
gether, the same name may pass in succession from B to (J; 
from C to D ; and from D to E ? ' 

The word ' damp ' primarily signified moist, humid, wrt 
But the property is often accompanied with the feeling 
of cold or chilness, and hence the idea of cold is strongly 
suggested by the word. This is not all. Proceeding 
the superadded meaning, we speak of damping a m 
ardour, a metaphor where the cooling is the only circnmst 
concerned; we go on stiii farther to designate tli«' iron 
that shuts off the draft of a stove, 'the damper,' tin; prii 
meaning being now entirely dropt. 'Dry' in like mai 
through signifying the absence of moisture, v. 
liquidity is applied to sulphuric acid com 
although not thereby ceasing to bo a moist, wet, or Liquid 
substance. 



404 GENERAL NAMES. 

The word 'letter* has undergone a series of transitions. 
Originally applied to the alphabetic characters, it passed to 
epistolary correspondence, to literature (letters) ; but in our 
post-ofliee system it has strayed still wider ; it has come to 
mean parcels made up of jewellery, soft goods, and miscel- 
laneous wares, provided they are carried by post. 

1 Gas ' is the popular name for any effluvia, anything in the 
air. Cloud aud smoke would be called gaseous emanations, 
although they are not properly aerial bodies. 

A * back: door ' originally the door at the back of the house, 
for servants, is applied to the door for the same purpose when j 
in front of the house. 

' Street/ originally a paved way, with or without houses, 
has been extended to roads lined with houses, whether paved 
or unpaved. 

'Impertinent ' signified at first irrelevant, alien to the pur- 
pose in hand ; through which it has come to mean, meddling, 
intrusive, unmannerly, insolent. So wide is the difference 
between the first and last senses, that, in spite of the apparent 
ease of the transitions, Mr. Eailey suspects the influence of the 
similarity in sound with the epithet 'pert* (Discourses, p. 
101). 

* Taste ' is transferred by similarity, or metaphor, from the 
feelings of the sense of Taste, to the feelings of Fine Art pro- 
ductions. There is also, in all probability, a transition in the 
double meaning of the w T ord in both employments, namely, to 
signify the pleasure imparted, and also the discrimination of 
bodies by taste, and of good and bad in Fine Art productions. 

Examples may be quoted from the highest questions of 
philosophy. Thus, the epithet 'beautiful,' properly circum- \ 
scribed by Fine Art, is often loosely applied to pleasures not 
artistic. 

This misleading tendency was never adverted to by either 
Plato or Aristotle, who, in their enquries, counted on finding 
under such words as Beauty, Cause, Justice, some unity of 
signification. The same mistake pervades Bacon's inductive 
enquiries. 

The word 'gentleman ' is an example of transitions growing 
out of historical and political circumstances. ' Meaning origin- 
ally a man born in a certain rank, it came by degrees to 
connote all such qualities or adventitious circumstances as 
were usually found to belong to persons of that rank. This 
consideration explains why in one of its vulgar acceptations it 
means any one who lived without labour, in another without 



TRANSITIONS BY SIMILARITY. 

manual labour, and in its more elevated signification it fa 
every age signified the conduct, character, habits and 
appearance, in whomsoever found, which, accordir ; 
ideas of that age, beloLged or were expected to 1 
persons born and educated in a high social position.' 

Similar changes are traceable in the worda * loyalty/ 4 vil- 
lain/ 4 pagan/ 

A ' convict ' properly means one convicted or found guilty ; 
but the signification most prominent is the trai 
state of hard labour entering into the punishment of convi 
felons. 

5. The derivations of terms frequently exhibit, in con- 
junction with contiguous transitions, an element of simi- 
larity. 

In an interesting chapter devoted by Mr. Mill to 'the 
Natural History of the Variation of the meaning of terms,' he 
notes two different tendencies to change both grounded in 
similarity — the one a movement of Generalization, the other a 
movement of Specialization. 

As to the first, the rendering of specific terms general, we 
have such examples as * salt ' extended from sea salt, to the 
class of saline bodies ; ' oil ' from olive oils to oils generally ; 
4 squire ' from the owner of a landed estate to other cla 
supposed to be entitled to a similar position ; * parson ' from 
the incumbent of a parish to clergymen at large. 

The Specialization of terms is apt to arise when people 
have occasion to think and speak oftener of one meml 
the genus than of the others. Thus ' Magazine,' a store or 
receptacle, has been narrowed to a periodical publication. 
\ Cake ' is specialized to pastry. A ' story ' is used to d 
nate a lie — a curious illustration of the frequent inaccuracy of 
current narratives. * Pleasure 1 has oftener the signifies 
of a very narrow class of enjoyments ; to which corresponds a 
special meaning of 'virtue' and virtuous. 'Wit' form 
meant intellectual power of any kind ; Bacon, Milton. 
Newton were great wits. The modern tendency is I 
it to the production of ludicrous effects, and even still Gu 
to the ingenious play upon words. 

6. The precautions to be observed in 
signification of terms, are these :— First, imp 
ings in current use, or meanings at the base of in 
predications, should not be disturbed , secondly, 
sociations of powerful sentiment should not be reversed. 



406 GENERAL NAMES. 

In restricting the word ' beauty ' to the refined pleasures 
of Art, and of the artistic element of Nature, we do not inter- 
fere with any received propositions, nor with the approving 
sentiment, connected with the term. The word * wit,' in its 
modern restriction, has undergone a much greater revolution, 
and certainly does not support the same propositions, nor the 
same associations of dignity as in Queen Anne's time. * Jus- 
tice ' cannot be accurately defined without a reterence, in the 
last resort, to law, authority, or command ; or at least to 
men's opinions as to what should be authoritatively enjoined 
or commanded ; a mode of defining that has always been un- 
palatable, as making the illustrious quality of Justice, the 
creature of law and opinion. 

* Civilization ' should, if possible, be so defined that the 
European nations should be included, and the American 
Indians, Bosjesmans, and aboriginal Australians excluded ; 
while no unfavourable sentiment should be introduced, by 
giving preponderance (as Rousseau did) to the supposed evils, 
or disadvantages, attending on the arts and discoveries of 
civilized nations. 

The difficulties attending the re-definition of a word are 
illustrated by the repugnance felt by many to Mr. Grote's 
view of the sophists ; a view that conflicted both with prevail- 
ing propositions and with feelings of dislike. A regard to 
truth or to justice may necessitate our violently interfering 
with a received usage. 

From the strong tendency to associate the word ' pleasure ' 
with the gratifications that border on vice, ethical theorists 
are hampered in using it to express the natural and legitimate 
end of human pursuit. They have to substitute for it, happi- 
ness, well-being, or other words of more feeble import as 
regards the zest and enjoyment of life. 

Mr. Mill adverts to cases where he thinks it might be a 
great misfortune to banish entirely the former meanings of 
words ; ^ inasmuch as the operation may involve the unfair 
predominance of a one-sided theory on some important ques- 
tions. He supposes the temporary prevalence of a selfish 
theory of* virtue, the consequence of which might be that the 
word 'virtue' would cease to connote disinterested conduct, 
and the very idea of such being dropt, the practice might 
degenerate accordingly. The remark, however, has no appli- 
cation to the words of obsolete physical theories, as 'epicycle/ 
' phlogiston,' ' vis viva, ' or to names that distort and confuse the 
phenomena expressed by them, as free-will and necessity, or 



DESCRIPTIVE TERMINOLOGY. 

to the names of infelicitous classifications, superseded by 

better. And in those changes of meaning adapted to 
press of science, as with the words salt, acid, 1; 
to drop entirely the earlier significations. 

7. The second Requisite of language is, Hint there sho 

be no important meaning without its word. 
This involves (I.) a Descriptive Terminal 

It is essential that we should be able to describe with oc 
acy ail individual facts and observations; consequently aa 
must be devised for all the known qualities of things whether 
physical or mental, and also mode* of signifying different 
degree whenever degree is taken into account. To describe 
the diamond, we need such names as crystal, refracting power, 
specific gravity, hardness ; and a numerical scale for stating 
the amount or degree of each property. Separate names are 
required for all our ultimate feelings and sensations. 

As regards the Object World, the fundamental experiei 
are the muscular states called Resistance and Motion, ami the 
Sensations — which, in the order of their objectivity, are bight, 
Touch, Hearing, Taste, Smell, Organic Sensations. 

The property called ltesistance has other names ; as Force, 
Inertia, Momentum. Gravity is a mode of the same property. 
The only farther requisite is a scale of Degree, which, in this 
instance, is given by the one perfect method — Arithmetical 
numbers. 

On the experience of movement, aided by sense, is grounded 
the object property called Motion, in all its varieties ; also 
Space, Extension or Magnitude, and Form. The varieti 
motion are quick and slow, regular and irregular, of this or 
form, and so on. Names are given to all the modes, and i\n- 
most, there are numerical estimates of degree. The sum 
marks apply to Space or Magnitude, which is pre-eminently 
open to arithmetical statement. 

Form is a property subject to great variations, and Qfti 
have to be found accordingly. The simple forms of Q 
— as line, straight, angular, curved, circle, triangle, sph 
cone, &c, are one department. The objects of nature 
have many others besides— heart-shaped, egg-shape I, p 
shaped. 

The language of Botany is most exigent of d I 

form. 

Colour has been expressed by assuming a 
of piima-y colours, and treating the rest as sb 



408 GENERAL NAMES. 

Thus, we have many different greens, blues, reds, yellows, 
greys; often characterized in the manner above described by 
quoting objects that exemplify them, sky blue, ultra-marine 
blue, apple green, blood red, French-grey. These names, 
however, do not define the colours; they do not from two 
simple ideas enable us to conceive a compound without refer- 
ence to the actual thing, they merely mark a species as distinct 
from other species. 

To make colour as far as possible a precise character in 
Mineralogy, there is a classified list, introduced by Werner, 
giving a name to every important variety of mineral colour. 
Eio-ht colours are chosen as fundamental, white, grey, black, 
blue, green, yellow, red, and brown, and under each of these 
is arrayed a list of shades. Thus, under ' blue ' are enumer- 
ated, — blackish-blue, azure-blue, violet-blue, lavender-blue, 
plum-blue, berlin-blue, malt-blue, duck-blue, indigo-blue, 
sky-blue ; ten varieties. Similarly for the others ; the number 
of shades being in some cases greater, in others less. 

For the scientific description of the outer or object world, 
the most essential properties are Magnitude, Form, Move- 
ment, Resistance (including all the modes of Force), and 
Colour. Kext to these in importance are Sounds, which also 
posess a terminology. The musical notes can be given 
numerically and symbolically ; all other varieties of sounds 
must be designated by distinct names, as melodious, har- 
monious, silvery, sweet, soft, harsh, grating, voluminous, 
silvery, wooden — names requisite alike in practical life, in 
science and in poetry. In the diagnosis of the chest, there 
are characteristic sounds, which receive appropriate names. 

Touch proper is cognizant of roughness and smoothness ; 
in combination with muscular feeling, it gives hardness, soft- 
ness, and elasticity (within limits ). The hardness of minerals 
transcends touch ; the harder body scratches the softer ; and 
a scale of hardness is formed upon this test. The pulse is 
estimated by touch proper, and besides the number of beats, 
names are applied to signify its tactile modes— as feeble, firm, 
wiry, steady. 

Tastes and Odours are provided with names. After indicat- 
ing the more general modes— sweet, bitter, pungent, we 
descend to the marked individualities, which are named chiefly 
(according to the most usual device for supplying terminology) 
from the substances where they are most marked — acid, 
alkaline, sooty, game, spirituous, oily tastes, garlic, spice, 
earthy, 



CLASS NAMES. 






The Organic Sensations— Acute pains, Bespiral 

Heat and Cold, Digestive feelings, &c, have a nom 

partly useful in every day lite, and still in 
volved in the medical art. 

Although the Sensations have all an object ref 
yet each contain subjective elements, becomr 
prominent as we recede from sight aud t 
almost the whole in the organic sensibilities. \\ 
designations are part of the subjective vocabulary, or 
vocabulary of Mind proper. This is completed by :l * 
designations for the Special Emotions; for the Will in 
various aspects — including desires, appetites, delibera 
resolution, belief; and for the Intellectual pr 
memory, reason, imagination, association, agreement. 

8. II. There is demanded next a name for every geo< 
notion, or distinct product of generalization. 

The previous demand is limited to the means of d. 
every fact belonging to either the object or the subject w 
The present relates more particularly to general notions or 
generalities. But though the two ends are different, the 
means are in great part the same. All the names of the 
Terminology are general names ; they mean qualities in 
general, although by their combination they can speeiiV 
individualize. Resistance, Form, Colour, Sound, T 
are general ; and their more specific modes heavy, round, blue, 
melodious, sweet, are also general. So that the Termim >] 
already contains a provision for expressing numerous ra 
of the generalizing operation. 

Still, the aim now propounded is so far distinct from the 
other, and may require to be separately considered and pro- 
vided. The results of generalization are of two kinds — da 
in the concrete, the subject-matter of the concrete sciences, 
qualities in the abstract, which are the characteristic Bab 
matter of the fundamental sciences — Mathematics, Pbj 
The names for the first department are not provided for DO 
Terminology ; thus, quartz, gold, oak, rose, fish, mammal, are 
radically distinct from hard, yellow, fragrant, warm — the one 
group comprises class names, the other the qualifv 
descriptive adjectives. 

The Terminology coincides much more nearly with the 
names used in the general sciences ; the notions of Math- 
tics, and of Chemistry (apart from the names #f the OOOd 
substances, gold, &c), are all more or less a part of the 
descriptive vocabulary. 



410 GENERAL NAMES. 

9. It is important that the names of generalities should 
be short. 

The discovery of the relations of general reasoning is facili- 
tated by the brevity of the designations. If we had to employ 
a long periphrasis lor distance, sqnare, gravity, body, it would 
be impossible to shape an intelligible notion of the law of 
gravitation, still less to combine it with equally lumbering 
expressions for tangential force, and for the resistance of the 
air, in considering projectiles. The advantages of methods of 
abbreviation are illustrated by the mathematical device of 
temporarily substituting, for a long formula that has to be 
treated as a whole, a single letter, a ; which relieves the mind 
of what would be a cumbrous impediment. 

De Morgan, with reference to the Differential Calculus, to avoid 
the tedious repetition of ' a quantity which diminishes without 
limit when A x diminishes without limit/ coined the word com- 
minuent. 

An important enquiry is started by Mr. Mill (Book IV., 
Chap. VI.),, namely, on what occasions we may safely use 
language as mere symbols, like the symbols of Algebra. 
Now, the answer to this question is obtained from the nature 
of such symbols ; they are signs of operation, adjusted by 
careful verification, so that no error can creep in if the rules 
are adhered to ; while the operations are all the more easily ; 
and rapidly performed that the things themselves are entirely 
kept out of view. On the other hand, in dealing with general 
names, class names, and terminology, we have to keep up a 
constant reference to the concrete things, as the only way of 
preventing us from incorrect assertions. After a proposition 
has once been carefully verified, as * Knowledge is founded on 
Agreement and Difference/ we seem to be under no farther 
necessity of referring to the concrete particulars ; which is 
true only until we begin to apply it. The Formal Logic 
shows us exactly how far, in matters of general reasoning, we 
may use language as mere symbols ; being to a certain extent 
analogous to Mathematics, although arriving far short of that 
science in the possibility of working aloof from all concrete 
meanings (See Appendix B.) 

10. In devising new general names, recourse may be 
had either to our language, or to foreign languages. Each 
alternative has its advantages and disadvantages. 

The advantage of deriving from our own language is being 
easily understood ; the disadvantage is the presence of mis- 



NEW TERMS. .1 1 J 

leading associations. * Damp ' would not be a 
apply to the gaseous form of water ; ■ vapoui ferable an 

being devoid of inappropriate connexions. When 
bach conceived that he had discovered an entin 
in nature, lie coined a word not belonging to any langi 
'odyl.' The generalization of Graham, comprehending 
stances of a gluey, or viscid nature, with flint, and niin 
of the glassy type (showing the conchoidel fracture) i 
pressed by the term ' colloid' (koWtj glue) ; the English 
being too exclusively confined to the viscid char. 
1 Inertia ' is a usefal word, although it demands to be 
against the too exclusive suggestion of passive r< 

11. The mere improvements of classified : re- 
quire new terms. 

This is the case with Graham's Colloids and Crystal!* 
which arranged previously known substances into a 
dichotomy, or contrast, founded on an extensive and important 
community of attributes. The improved classifications of 
minerals, plants, and animals, required new terms, monocotyle- 
don, perianth, inflorescence, mammalia, infusoria, &c. U 
to the imperfection of the contrast ' mind and mi- 
psychologists have introduced the terms ' subject ' and ' object' 
as exhibiting the antithesis in greater purity. 

12. By adapting old names, we may be often saved t 
a new coinage. 

The creation of new terms is sometimes wanton and m 
less. When there is no new meaning, no fresh product of 
generalization, the adding of new terms is not justified upon 
slight pretexts. Apart from increasing the alrea 
burden of language, there is the more serious evil of leading 
people to suppose that there is a new meaning. S»me ot 
Kant's innovations in language are obnoxious to this criti. 
His 'analytic' and 'synthetic' judgments 'a priori' and 4 a 
posteriori' have some advantages as synonyms, bat the m 
ings had been already expressed. 

A little management may often get over the insufii 
the existing* names. The evil to be complained of is, t 
popular name does not exactly square with 
ing ; thus the words, force, resistance, motion, admit 
ation, are adopted into science ; while the popular 
so far from suggesting, are at various points in con 
the scientific meanings. Even in such circni 



412 GENERAL NAMES. 

adherence to the popular words may be a less evil than new 
coinages. The precautions accompanying the use of old 
names are these : — 

(1) The words may, at the outset, be defined according to 
their sense in the particular science. Thus, the mathematician 
defines a point, a line, a square, a cone, a spiral ; the physicist 
defines inertia, force, velocity, attraction, liquid, lever, air, 
heat, &c. 

The chemist defines element, compound, affinity, solution, 
decomposition. The botanist gives the name ' fruit ' to all 
seed-vessels. The biologist defines life, respiration, digestion. 
The psychologist defines sensation, idea, memory, association, 
reason, emotion, sentiment, passion, conscience ; all which 
terms are liable to the loose and uncertain meanings of com- 
mon speech. The political philosopher defines government, 
nation, law, order, progress. These various terms being 
consistently used, in accordance with the several definitions, 
they are known to possess the significations indicated, and no 
others, within the sphere of their respective sciences. 

This plan was followed in framing the language of Geometry. 
Names were usurped from common speech, and used in 
peculiar senses defined at the beginning of Geometrical trea- 
tises. Thus a * sphere ' (acjxupa), was originally a playing 
ball, a ' trapezium ' (jpaire^tov), a table; but, the scientific 
sense being defined at the outset, and rigidly adhered to 
throughout the demonstrations, there was no danger of con- 
fusion between the popular meaning of the words and the 
mathematical. 

(2) We may employ, in science, the precaution required in 
composition, with reference to names having plural meanings, 
which are abundant in all languages ; namely, so to place and 
fence each word as to keep back all the meanings not in- 
tended. The word ' moral' has various distinct significations ; 
yet the use of it in any one place may be such as to admit 
only one. When we speak of ' moral suasion,' we exclude the 
meaning of right and wrong, and indicate only 'mental ' as 
opposed to physical. < The morality of the act was question- 
able,' shows that moral rightness is intended. 

(3) The device of stating the contrary of a term has been 
seen to be highly effectual in saving ambiguity. ' Reason and 
not passion prevailed ' indicates that ' reason is intended in 
the peculiar sense of ' motives resulting from rational calcula- 
tion of the future.' 

13. III. In addition to a Terminology, and names for 



NOMENCLATURE. 

all important Generalities, there are n • the 

purposes of Classification. 

This is Mr. Mill's third class under the Second Ri 
a Philosophical Language. It 




grades — the Classes, Orders, and Genera- 
lised ; but since the nnmber of the ol 
descend, while in Botany and in Zoology, the Iow< st kind 
species amount to many thousands, an abbreviating (lev 
employed, namely, to retain the name of the genius, and d 
nate the species by a qualifying adjective — * Orchis □ 
The saving of language is not the only advantage oi 
double-name ; there is the additional edect of imparting the 
knowledge of the genus that the species belongs to, and 
the mark or character dividing it from the other e 
the same genus. Thus, a name so made up gives the 
the species in the classification, so far as effected bj 
the genus. The operation could have been carried farther, so 
as to include the Family or the Natural Order ; thus the \ 
mon daisy would be ' Composite bellis perennis.' But this 
would be held too burdensome. 

Under the same head is included the double naming in 
Chemistry — sulphate of potash, or potassic sulphate. T 
designations, however, although serving to impart informal 
respecting the substances named, are formed upon a principle 
quite different from that above explained with reference to the 
Natural History sciences. They belong to the special peculi- 
arity of the science of Chemistry — the distinction of snbstai 
into Simple and Compound, and of Compounds into dill* 
modes and degrees of union ; and in the case of con 
they indicate the supposed elements and manner of cum; 
tion ; * protoxide of iron,' states that the substance l 
compounded of oxygen (in a certain measure) and iron. 
is scarcely more than an analogy between this el 
significant names and the double names of I! 

Double naming has not been admitted into 
Professor Nicol remarks that the science is not 
the change. In point of fact, however, Mineral 
nature more nearly allied to Chemistry thin I 
Zoology; and the double naming if used wou 
species, but for varieties ; thus ' magnetic iron ' would W I 



414 GENERAL NAMES. 



. 



a proper specific designation ; the snbstance named has 
chemical expression, which will always be preferred. 

Expressive names may be employed, apart from any system 
or rule, in all subjects. Thus, in the Natural Orders of 
Botany, we have such names as ' Compositse,' ' Umbelli ferae,' 
which incidentally inform ns of some of the characters of the 
families named. So, the names of the orders of Birds are all 
expressive of some leading feature. 

Whewell proposed to reserve the title 'Nomenclature ' for 
the designations that we have now been considering. Linear, 
lanceolate, oval, or oblong, serrated, dentate, or crenate leaves, 
are expressions forming part of the terminology of botany, 
while the names ' viola odorata/ and ' ulex Europseus ■ belong 
to its nomenclature. 



CHAPTER IIL 
CLASSIFICATION. 

1. The Methods of Classification grow out of its ends. 

I. The sequence of the Descriptive characters should 
follow the order of the properties as expounded in the 
department. 

Considering that a natural kind or species — mineral, plant, 
or animal — may have ten, twenty, or fifty characters, great im- 
portance attaches to the method of stating them. When we 
seek for a principle to govern this arrangement, we find it in 
the order of the properties in the general exposition of the 
science or sciences where they are discussed. Mathematical 
properties would naturally precede physical, physical would 
precede chemical, and so on. In an organized being, the 
tissues precede the organs ; and some organs precede others 
upon the reasons assigned as governing the scientific arrange- 
ment or classification of knowledge. 

Every classifying science has "two divisions— one General, 
the other Special. The first or General division explains the 
characters to be used in describing the species, and expounds 
them more or less minutely. The second or Special division 
comprises the detail of the objects, and assigns to each its 



SEQUENCE OF CII.YIIA 

share or participation in these chai 
the objects. 

Thus, in a work on Mineralogy, the General I 
prises Crystallography, or the Forms of Minerals; the / 
Properties, as Cleavage, Fracture, Hardness, Ten 
Gravity, Optical Properties, Heat, Electricity, Mo 
Chemical Properties, as Chemical compi 
This division is an abstract of Molecular Pn 
try. The Special Division, named Description i 
the detailed account of all known minerals, according 
properties. For example, Quartz is described as 
certain Crystalline form, a peculiar Cleavage, Fracture, 6 

So in Botany. The First Division comprises Strnc 
and Morphological Botany, or the parts of the plant generally 
— Tissues and Organs — stated on the methodical plan of 
ceeding from the general to the special, the less dep 
the more dependent. The Nutritive Organs have pn 
of the Reproductive ; their sub-divisions are taken in the i 
— Root, Stem, Leaves. The Division is completed by the 
functions or Physiology of the different tissues and organs. 

The Second Division is the Classification and Description of 
Plants^ The complete account of each species then properly 
accords with the order of the exposition of the constituent 
tissues, organs, and functions, in the First Division. 

In Zoology, the method is still the same, although not so 
thoroughly carried ont as in Botany, on account of the greater 
complications. 

Care should be taken to distinguish ultimate from derivative 
characters. The Description is fully exhausted by a complete 
enumeration of what are supposed to be ultimate chara< 
The derivations or deductions from these, if given, should bo 
given as such. A character is to be provisionally receive 
ultimate, if it cannot be reduced nnder any more 
character. 

For example, the snpport of combustion is 
character of oxygen, and does not rank with the 
present held to be ultimate, namely, the sn< 
the specific heat, electro-negative position, the comb, 
power generally. 

2. II. Observing the golden rule, we inn 
gether, in classes, The things that n the 

greatest number of important attribul 

At the outset of the present department of Logic— Di: fin i- 



416 CLASSIFICATION. 

tion, it was necessary to state with regard to the formation of 
classes of things, that preference is to be given to such groups 
as contain in common the greatest number of important attri- 
butes. This applies to all the modes of dealing with the Con- 
cent or Notion. The mind sees objects to most advantage 
when it views together those that have the greatest number of 
affinities. 

It is on this principle that the vertebrate animals have been 
classed according to the leading points of their Anatomy and 
Physiology, such as the manner of bringing forth their young, 
rather than according to the element that they live in (earth, 
water, air). The bat flies in the air, but has more real affinities 
with quadrupeds than with birds ; the whale, seal, and por- 
poise, have warm blood and suckle their young like land 
quadrupeds, although living in the sea as fishes. 

The importance of the attributes is to a certain extent 
governed by the end in view. For* practical purposes, whales 
are classed with fishes (as in speaking of the whale fishery) y 
because their living in the sea determines the manner of their 
being caught. So, food plants, esculent roots, fruit trees, are 
groups practically important, but do not coincide with the 
classifications of botany. 

With a view to theoretical science, whose purpose is to 
assemble in the smallest bulk, and in the most intelligible and 
suggestive arrangement, the greatest amount of knowledge, . 
the golden rule must be strictly carried out. Even for practi- 
cal ends taken collectively, this is the most useful plan, from 
the very reason that it does not defer to any one end in parti- 
cular. The classifications for practice do not supersede the 
classifications for knowledge, but are additions to these ; they 
occur in the practical or applied departments of information, 
as Medicine, Commerce, Law, &c. 

Not only in forming groups, but in their juxtaposition in the 
consecutive arrangement, regard is paid to the amount of affinity. 
The Natural Orders of Plants and of Animals are so placed, 
that any two lying side by side are more nearly allied than 
any other two that could be fixed upon ; and alterations are 
constantly suggested to give proximity to the closest alliances. 
Thus, Mr. Huxley argues in favour of an arrangement uniting 
the Proboscidia with the Rodentia, rather than with the Artio- 
dactyla and Perissodactyla ; the singular ties that ally the 
Elephants with the Rodents having been a matter of common 
remark since the days of Cuvier. 

3. In aiming at a Natural Classification, that is, one 



MAXIMUM OF AFFINITY. .J 1 7 

based on the maximum of important agreements, we 
meet with alliances on different sides, of nearly equal 

value. 

Different groups may touch each other at diff 
and may have equally strong alliances. Thus, in II • 
natural order SoZawacece, if viewed with reference to i 
(the female side), allies itself with Scrophulai 
with reference to the stamens and corolla (the male Bide} it 
allies directly with Orobanchaccce. 

Various considerations may be brought forward to di 
mine the choice under such circumstances. One m 
cast groups into a circular classification, wherein the bui 
sion may return to itself. Another mode is an arrangement 
in two directions, as in a square ; an idea carried still farther, 
although in practice scarcely workable, by a cubical arrange* 
ment. 

It may, moreover, be considered which method would bring 
about the maximum of alliance on the whole, or with r 
ence to the entire classification from first to last. Jn 
search after this maximum, we may have to be content with 
occasional juxta-positions of inferior degrees of resemblance. 

Yet farther, we may make provision for double placing of 
the same group, with a view to comparing it on all sides with 
its congeners. 

4. In Zoology, the most natural classification, on the 
whole, corresponds very nearly with a serial ;ord- 

ing to the degree of development of Animal Life, and thus 
facilitates the discovery of laws by the Method of Con- 
comitant Variations. 

The great divisions of Invertebrate and Vertebrate, and tho 
sub-divisions of each, represent a gradual rise in the scale ot 
being. The Radiata, as a whole, are lower than the A 
lata ; the Fishes are the lowest, and the Mammalia the big 
class of the vertebrate type. There are deviations from 
gradual rise in organization. The fish named amph 
lancenlatus is surpassed in complexity ot structure 
insects and molluscs. 

For plants, the method is much more qualified. T 
wide interval between the lowest Fungi 
Dicotyledonous Natural Orders, but there is no line 
progression. The Monocotyledons are not thro 
inferior grade to the Dicotyledons, nor is there a : 



418 CLASSIFICATION. 

among the Natural Orders of either division. The application 
of the method of concomitant variations is still possible, al- 
though greatly limited. It can be seen that the absence of 
the inflorescence in the inferior plants is conjoined with tbe 
cellular structure, which is the lowest organization of the 
tissue of the plant. 

The serial order would apply to all kinds of objects where 
there is a progress or development, and where the property 
developed has a commanding importance. Thus, Social in- 
stitutions, as Governments, may be classed according as they 
approach to the most perfect type. 

The Races of Men, viewed with reference to mental endow- 
ment, lie in an ascending scale, with such occasional exceptions 
as the possessing of some one faculty in a higher grade by a 
race inferior on the whole. We can thus study the concomi- 
tant circumstances of superiority and inferiority in mental 
development. 

Civilization in its larger leaps is linear, but in the minuter 
differences, not so. Communities advance in special direc- 
tions, the progress in one line being often accompanied by 
backwardness in others, from the limitation of the human 
energies as a whole. It is true of modern as of ancient civi- 
lized peoples, that each has its own peculiar excellencies and 
defects. 

Excudent alii spirantia mollius sera 
Credo equidem, vivos ducent de marmore vultus ; 
Orabunt causas melius, coelique meatus 
Describent radio, et surgentia sidera dicent : 
Tu regere imperio populos, Romane, memento ; 
Hae tibi erunt artes ; pacisque imponere inorem, 
Parcere subjectis, et debellare superbos. 

5. III. It is an end of classification to save repetition 
in the description of objects ; for which end the generaliza- 
tion is made by successive steps, halting-places, or grades. 

Instead of describing the species ' elephant ' by all its 
characters, beginning with extension and materiality, the 
naturalist mentions as specific marks only a small number, and 
refers to the rest by a series of names expressing what is com- 
mon to it with other groups. 

Whenever two or more individuals agree, the agreement 
may be stated once for all, and only the difference given under 
each. In characterizing the races of men, we state first what 
is common to the whole, and next what is special to each 



GRADES. 

taken apart. We might apply tlio method fo any fw 
that contain agreements peculiar to thems< ' 
natural limit to the process but the existen 
The number of grades may be carried to any length, 
as there is a basis of community. The more compli 
objects, that is, the more extensive the compass of i! 
butes, the farther may the gradation he carri 
fieance of the points in common might be a n 
treating them as resting-points of the gradation. 

In Botany there are four principal stages, marking 
Families, or Natural Orders, Genera, and S] 
maintained throughout ; while, as occasion arises, intermediate 
grades are constituted. (See Part First, p. 05). 

In Zoology there is first the grand division of iNVEETEl 
and Vertebkata. The Invertebrata were divided by Cuvier into 
Radiata, Articulata, Mollusca, whose farther subdivisions 
termed Classes (Infusoria, &c). The Classes contain 
or Natural Orders, under which are Genera, and under 1 
Species. There- are thus six regular halting pi 
the individuals and the summum genus — Animal. The verte- 
brate Animals descend at one leap to Classes (Fishes, Rep 
Birds, Mammalia). The class Fishes undergoes a divi 
into Cartilaginous and Osseous ; under which are the Natural 
Orders. The Reptiles, Birds, and Mammalia are occasionally 
broken up at once into Natural Orders. 

The carrying out of the classificatory arrangement demands 
that by the methods of Definition, the agreements at 
stage should be thoroughly ascertained, and fully and prec 
stated. The classification by grades is a useless formality if 
the corresponding characters are not given. The cbeu 
division of simple bodies into Metals and Non-metals is 
should be) accompanied with the characteristic marks or 
common properties of each class. The farther sub-division of 
the metals into Noble Metals, &c, is seldom followed np 
rigorous enumeration of all the points of community : 
only advantage gained is the mere proximity of the re 
bodies. The same incomplete adoption of the for: 
grades is found in the classification of Dl 
chorea, tremor, hysteria — are classed together, but 
the enumeration of common characters. 

6. The statement, b) successive gra 
of community, is suited to the discovery of L 
comitanca 



420 



CLASSIFICATION. 



In ascertaining whether a property a is uniformly conjoined 
with a property /, there is an advantage in being able to 
separate the cases where a is absent from those where it is pre- 
Bent. This is done in the system of grades. Thus, by isolating 
the order Ruminantia, we readily discover the concurrence 
of rumination with cloven hoofs. 

If there were any laws of concomitance among the proper- 
ties of the metallic or the non-metallic bodies of Chemistry, 
they would best appear in the study of the groups formed upon 
special properties. Thus, when the metallic substances are 
viewed together, they readily disclose any conjunctions with 
metallic peculiarities. So in the non-metallic division, the 
halogens — Chlorine, Iodine, Bromine, Fluorine, present a nar- 
rowed field of conjoined properties. 

7. The classifications of Natural objects are understood 
to terminate with the Species, or lowest Kind ; and thus a 
high importance attaches to the defining marks and 
boundaries of Species. 

In Botany and in Zoology, the view had long prevailed that 
a species was marked off by community of descent, while any 
differences that might arise between the descendants of a 
common ancestor were regarded as varieties and not as specific 
differences. 

The doctrine of the absolute fixity of species is now called 
in question, and proofs are offered to show that, in the course 
of descent, differences called specific may arise among the 
descendants of a common stock. This leads to a modified 
statement of the doctrine of species. The fact still remains 
that some characters have a high degree of constancy or per- 
sistence through successive generations ; while others are 
liable to change. 

"Wherever a line can be drawn between highly persistent 
and highly fluctuating characters, we may call the first specific 
characters and the others mere varieties. Thus, in numerous 
species, both of plants and animals, colour is liable to consider- 
able variation within limits. So the absolute size of living 
objects may alter greatly. Also the degree of any quality or 
endowment, as the strength, or sagacity of an animal, may 
change. But the tissues, organs, and structural arrangements 
persist through many successive generations. 

Importance may, nevertheless, be still attached to the fact 
of the fertility or infertility of the unions of individuals. The 



SPECIES. 

horse and the ass are fertile for one generation, bat the 
is incapable of farther procreation. 

In Minerals, the boundaries of species are fixed B 
regards crystallization and chemical composition, and all 
consequences of these properties. As regards compounds, 
chemical, which may take place in all proportions, thore 
be no fixed lines, although a lew grades may be assigned with 
doubtful margins. 

In Diseases, the presence of certain fixed characters, such as 
the leading symptoms of Inflammation, of Small-pox, of Gout, 
offers distinctions that may be called specilie. 

8. In fixing the boundaries of Species, respect may be 
had to the number as well as to the persistence of the 
characters. 

The Infima Species or lowest kind, in any of the Natural 
Kingdoms, is in certain instances divided from all other sp 
by a large number of properties, known and unknown. The 
characters of the species 'horse ' are very numerous : of man 
still more so. There cannot be the same extent of specific 
distinctions in the inferior animals ; nor in more than a small 
number of plants. Still, the existence of as many as three, 
four, or six distinguishing marks, all of some importance and 
constancy, would suffice for making a species : while the 
limitation to one or two might leave a doubtful choice between 
Species and Variety. 

Mr. Mill puts the question, are all the classes, in a Natural 
Classification, Kinds ? He answers, certainly not. ' Very few of 
the genera of plants, or even of the families, can be pronounced 
with certainty to be Kinds.' In point of fact, the difficulty would 
be to fix on any class of the higher grades, whose properties 
numerous as to rank them with differences of Kind (understood in 
Mr. Mill's perhaps over-strained language respecting the Infitna 
Species). 

Another question raised by Mr, Mill is the propriety of WnewelTl 
allegation that 'Natural groups are given by Type % and not by 
Definition.' By a Type, Whewell meant a well-selected av< 
member of a class, removed alike from all extremes; a concrete 
embodiment of the class, to be used for purposes of identifier 
in preference to any verbal definition. The motive was tin i 
ence of anomalous members of many groups in Natural Hi 
which neither conform to the verbal definition nor yet differ 
ciently from the other members to be excluded from I 
We may imagine a grcup formed upon ten character 
sisting of individuals that vacillate, some upon on< 
eome upon another, while yet agreeing in by far 1 I.e. ad • r. 



422 CLASSIFICATION. 

We may even make the extreme supposition that the vacillation is 
such that no single character of the ten persists in every indi- 
vidual ; hence, in strictness, there would be no common feature, 
and yet there would be a very large amount of resemblance. 

In commenting on AVhe well's mode of getting over the difficulty, 
Mr. Mill re-iterates his view of distinctions of Kind, which, when 
fully complied with, can leave no such uncertainty as is supposed. 
Moreover, he remarks that a class must possess characters, that 
these characters cannot be arbitrary, and must admit of being 
stated, which is tantamount to Definition. 

Probably Whe well's difficulty might be met by the allowance of 
a doubtful margin, which has been seen to be essential in cases of 
continuity far less complicated than the demarcations of groups in 
Natural History. 

9. The arrangement of descriptive characters by grades 
gives the greatest amount of knowledge in the least corn- 
pass. Yet, for practical objects, it may be desirable to 
bring together, in consecutive detail, all the characters of 
a given species. " 

The genus and species, 'Man' in the class mammalia, is 
described by the Zoologist, like all the other animals, by giving 
a certain number of characters at each stage — those common 
to Vertebrate Animals, to Mammalia, to Bimana (of which 
man is the sole representative), and finally the marks peculiar 
to the species. But the human anatomist treats Man in the 
pure isolation, disregarding, except incidentally, his place in 
the animated series. So, from the importance of the species 
* Horse/ there is afforded a similar exhaustive Anatomy. 

Complete Monographs of important species are not only 
useful for practical ends ; they are also the constituent 
materials of Zoology. 

10. IV. The statement of characters proceeds, in the 
last resort, upon a close comparison of Agreements and 
Differences. 

^ From the nature of knowledge, the highest degree of intelligi- 
bility depends upon the most complete exhibition of agreement 
and of difference. 

The classification by grades provides for stating Agreement. 
A grade, whether Class, Order, or Genus, is defined by the 
points of agreement discovered among its members. The 
Botanical class ' Dicotyledon/ has a certain structure of Stem 
and of Seeds. The Animal genus < Ovis,' has, as common 
characters, Horns of a peculiar kind ; Hoofs compressed ; 



STATEMENT OF CHABACT1 

Afammce two ; Chin beardless; region between the i 
nostrils convex. 

When characters are stated shortly, as by a mere \. 
or phrase, the tabular method is the most eff 
minerals. In larger descriptions, the headings ;tt least .should 
Btand out distinct. Thus, the genus ' Poppy ' is discriminated 
(from the other genera of the Poppy Family) on fcwo 
etie referring to the capsule, the other to the flowers. The 
generic agreements may be presented to the eye thus : — 

1 Capsule, Globular, ovoid or slightly oblong, crowned by a 
circular disk, &c/ 

1 Flowers. In Size, rather large ; in Colour, red, white, (in 
the British species) purplish, or (in some exotic ones) pale 
yellow.'* 

The greatest difficulty and nicety belongs to the statement 
of Differences. Only in dichotomies can this be accomplished 
to perfection. When a genus has two species, we can put 
them against each other, according to the plan observed in 
defining by antithesis or contrast (see p. 164). Thus, in the 
genus * Corydalis ' (of the Fumitory Family), there are two 
species (Yellow and Climbing). Their differences admit of 
pointed contrast as follows : — 

Yellow Climbing. 

Stem. 
Short, erect, branched Long, climbing, slender. 

Flowers. 
Yellow Whitish. 

If on any one part, there are plural contrasts, the presenta- 
tion might be varied thus : — 

q . J Short, erect, branched — Yellow 
btem^ Lon ^ clim bi ngj slender — Climbing. 
"When there are several species, the presentation cannot 
always be effectively given in this manner ; some may contain 
agreements among themselves, as well as differences, which 
would perplex the contrast. We may, however, occasionally 
mark off any one from all the rest, thus : — 

♦Modified from the following description in Bxxtham'i British 

'CapTule globular, ovoid or slightly oblong, crowned by a circular 
upon which the stigmas radiate from the centre, interna ly divided i 

to the centre, into as many incomplete cells as there - 
ing in as many pores, immediately under the disk. I 
red, white, or purplish in the British species, or pale yelloi in some 

exotic ones ' 

19 



42 1- CLASSIFICATION. 

Opium Poppy. Other Species. 

Plant 
Glabrous Stiff hairs 

Colour. 
Glaucous Green 

Leaves. 
Toothed or slightly lobed Once or twice 

pinnately divided. 
We may always select for pointed contrast the two classes 
that are most like, and therefore most liable to be confounded. 
This is done incidentally (although not with systematic thorough- 
ness) in all the classificatory subjects — Minerals, Plants, 
Animals, Diseases. Thus the Silk-cotton order of Plants 
( Steradiaceos) resemble Malvaceoe in their general characters, 
particularly their columnar stamens, but differ in their two- 
celled extrorse anthers. * In their properties, Capparids 
resemble Crucifers' (difference not stated). The genus 
Ranunculus is distinguished from Anemone by the want of the 
involucre. In the Field Poppy, capsule globular ; in the Long- 
headed Poppy, capsule oblong. 

11. V. It being requisite to a Natural Classification thai 
bodies be arranged under deep and inaccessible affinities, 
a separate scheme, of an artificial nature, must be provided 
as an Index. 

A classification may accord with the primary rule, and may 
be defective in the means of discovering the place of a given 
object. The determination of a plant is puzzling to the beginner 
in Botany. Now, it was a merit of the Linnaean system 
to make this comparatively easy; and the advantage was 
sacrificed in the adoption of a Natural system. 

The ideally best classification is one where the properties 
common to the members of the several groups are both im- 
portant and obvious. Such a combination is at best but 
partially realized. Thus, in animals, the important affinities 
are so far internal, being disclosed only on dissection, as those 
referring to the minute points of the skeleton, the nervous 
system, the structure of the viscera, &c. ; and so far external, 
as the form, the external divisions, the integument, and 
(partly) the reproductive organs. It is fortunate for Zoology 
that these external peculiarities either constitute of themselves, 
or are marks of, the important affinities. Still, they are not 
the whole, and even if they were, a scheme must be formed to 
guide the student in following them out to the determination 



INDEX CLASSIFICAIIO 



of the name and place of the individual. 
yet been afforded in Zoology. Yet, without it the i 
snraraate natural arrangement must be a scale. 1 bo 
but proficients in the detailed knowledge of animal 

Chemistry (with Mineralogy) is in a still \ 
governing principle in arranging chemical compounds I 
their chemical composition, which is indiscoverable by tho 
naked eye, the determination of a specimen is impracti 
without an artificial Index. Owing to the greal imporl 
of discriminating substances chemically, in the i 
is provided, known as Chemical Testing or analysis, wh< 
the student, with a limited knowledge of the entire 
Chemistry, can yet determine a large number of bod 

In Botany, the Index Scheme, or Analytic Key, is highly 
elaborated. It consists of tables based upon a bucc 
properties, there being under each a bracket contai 
(rarely three or more) alternatives. (See Book V., I 

In a case of equal importance to Chemistry, the i I 
of Disease, an Index classification is still a desideratum. 
medical student has no aids to the discrimination of dis 
short of an aquaintance with diseases generally, after a tail 
study of Pathology. The mode of preparing an Index scheme 
could be readily gathered from the plans pursued in Botany 
and in Chemistry. 

LOGICAL DIVISION. 

12. The rules laid down for Division, as a Logical Pro- 
cess, are rules of Classification, of which Division, in the 
Logical sense, is merely one aspect. 

There are many ways of dividing a whole or aggregate into 
component parts. A concrete or individual ohject, as 
Minster, may be divided into choir, nave, and transepts ; into 
main building and spire; into walls and roof ; into the 
for public worship and the private apartments. r IV 
crete partition, or dismemberment. In much the sa 
an ox is divided for consumption. Again, a concre 
is mentally divided, or analyzed, into its abstract elen 
may separately attend to the form, the size, the brill 
weight, of the diamond. This is Abstraction. Whenaploi 
of forces concur to a certain result, they often req 
studied in separation ; thus, in mechanics, we 1. mpute 

moving power and friction apart ; in astrononv 
ing forces are computed separately, and then compounded. 



42G CLASSIFICATION. 

This is Analysis and also Deduction, or Deductive Combination 
(See INDUCTION, Deductive Method), and is one of the most 
familiar of scientific operations. 

Logical Division is different from any of these modes of 
separating wholes or combinations into parts. The received 
roles enable us to judge of its precise meaning and compass. 
They are the following : — 

(1) 'Each of the parts must contain less than the thing 
divided.' 

(2) * All the parts together must be exactly equal to the 
thing divided/ 

(3) ' The parts must be opposed,' that is, 'mutually exclusive.' 
Hamilton adds (4) ' The principle of Division should be an 

actual and essential character of the divided notion ; and the 
division, therefore, neither complex nor without purpose.' 

These rules point to an actual, exhaustive, single-pur- 
posed, and important division. The first rule points to an 
actual division, for unless the parts be less than the whole, 
the whole is not divided. The second rule supposes that the 
parts are to be exhausted, so that we may declare everything 
contained in the whole to be found in one or more of the 
parts. There may be divisions where this is not insisted on. 
The third rule requires that the division shall be upon one 
purpose or plan, so that the parts may be mutually exclusive : 
we divide an army into infantry, cavalry, and artillery ; or 
into officers, non-commissioned officers, and rank and file ; 
but not into infantry and commissioned officers. The fourth 
rule indicates that divisions should not be on trivial or insig- 
nificant characters, as if we were to divide an army or a popu- 
lation into persons with names of one syllable, and persons 
with names of more than one syllable. 

The real importance of these rules is with reference to 
Classification ; for other purposes they are idle, and even 
erroneous. When a comprehensive class, as Vertebrata, has 
to be sub- classed, we must comply with the conditions of 
classification generally, or such as we observe in the march 
upward, from the lower to the higher grades. The Vertebrata 
are divided or sub-classed into ^Fishes, Reptiles, Birds, and 
Mammals; it being obvious that each sub-class is less than 
the whole, that all the four sub-classes amount to the whole ; 
and that each sub-class excludes all the rest. If there were a 
failure on any of these points, the classification would be bad ; 
the field of the sub-divisions is supposed to be exactly the 
field of the entire group ; nothing is to be left out, and nothing 



LOGICAL DIVISION. 

counted twice. So in every case of genus and species. If 
we mean to give all the species, we should give bhem a,ll. 
Moreover, a division into species, where the same individvala 
appeared in two species, would confound the very id< 
specific distinctions. If the bat were placed among bird 
also among mammals, there would be two conflicting principles 
of classification. 

Division, in the logical sense, is thus merely a way of 1 
ing at classification by grades. Hamilton's additional rule- 
that the principle of Division should be essential and important 
— is the golden rule alike of defining and of classifying. 

A division, or sub-classification, is complete when we may 
disjunctively affirm a member of the class as in one or otb 
the parts ' Actions are either good, bad, or indifferent, ' sup- 
poses that Actions may be exhaustively and correctly div 
or sub-classed into good, bad, and indifferent ; it being under- 
stood farther that the same action is not both good and bad., 
good and indifferent, or bad and indifferent. 

A classification may be conveniently tested by the rul< 
division, especially the third, the violation of which makes the 
Fallacy of Cross-division. Thus, the old classification or 
division of the Virtues, called the Cardinal Virtues — Justice, 
Prudence, Courage, Temperance — is vicious ; and the vicious- 
ness may be expressed as either a bad classification or as an 
illogical division ; for Prudence includes the whole of Temper- 
ance, as well as all that part of Courage that conduces to 
self-interest. 

The Analysis of a Compound is necessarily exhaustive J 
it is the purpose of analysis to ascertain everything that 
enters into the given combination. A chemist examines a 
meteoric stone, with a view to determine all the chemical 
elements present. The physiological chemist desires to find 
out all the constituents of blood, of bile, of gastric juic 
flesh, and so on. To such cases, the rules of Division might 
apply, if anything ever turned upon them. 

The ultimate analysis of the Mind, whether in whole or in 
part, might be tested by logical division. Tims, .Mind 
whole is divided into Feeling, Volition, and Intellect ; ai 
this division the logical tests should apply. The thn 
ments should exhaust the mind without going beyond 
they should be mutually exclusive. So in the Int. 
analysis into Discrimination or Difference, Agreement 
larity, and Retentiveness, professes to be an ultimate 
the three functions ought to contain all that is intellectual 



428 CLASSIFICATION. 

nothing more ; while each should contain nothing in commoi 
with the other two. The old enumeration of the Intellectua 
powers— Memory, Conception, Abstraction, Reason, Judgment 
Imagination — is not a logical division ; it could not be showr 
to be intellect, all intellect, and nothing but intellect; whik 
the members are not mutually exclusive ; memory has some- 
thing in common with all the rest. 

13. Logical Division fails in classifications with undefined 
boundaries. 

The rules of Logical Division are inapplicable to classifica- 
tions growing out of combination, growth, or development. 
Such are the compounds of chemistry, the offspring of living 
bodies, the developments of human knowledge, the associative 
growths of the mind. All these products are naturally un- 
limited and inexhaustible. Oxides,' carbonates, silicates, 
alkalies, ethers, are interminable ; their particulars cannot be 
enumerated ; no enumeration necessarily takes in the whole. 

In the Human Mind, the Senses, or primary elements of 
sensibility, comply with the rules of Division. The Emotions, 
most of which are growths or developments, do not comply 
with it. If any of the emotional states were strictly ultimate, 
they would be mutually exclusive ; but there are very few 
such ; Wonder, Fear, and Love, are nearly ultimate, but may 
not be wholly so. The great bulk of the Emotions being 
growths out of common elements, they cannot have a strict 
mutual exclusion ; yet they may have distinctive characters, 
and may be properly viewed as emotional species. Love, Self, 
Power, Irascibility, Pleasures of Knowledge, Beauty, Moral 
Feeling — are all well-marked groups of emotions, but they are 
formed out of common elements, which are perceptible to our 
self- consciousness. As products of growth or association, they 
have no fixed number ; new occasions would give rise to new 
varieties or species ; and there cannot be a mutual exclusion. 
They are subject to the golden rule of classification, but they 
do not present a case for logical division. 

There is a similar inapplicability to the classification of the 
Sciences ; these also succeed one another by growth or develop- 
ment. Chemistry involves Physics, and Biology, Chemistry. 
The Natural History sciences — Mineralogy, Botany, Zoology, 
Geology — are full of unavoidable cross-divisions and double 
entries. In such a science as Materia Medica, there are many 
double entries ; the same substance is at once stimulant and 
narcotic. The Social Sciences — Politics, Political Economy, 
Jurisprudence— cannot be made mutually exclusive. 



BOOK V. 

LOGIC OF THE SCIENCES. 

To exhibit the principles and rules of Logic in a new 
aspect ; to indicate the fields where these are most ne 
and where examples are provided with inexhaustible ful- 
ness, — we shall review in order the Theoretical Sciences, 
and some of the leading Practical Sciences. 



CHAPTER I. 
LOGIC OF MATHEMATICS. 

1. In Mathematics, logically viewed, there is afforded 
the most consummate exemplification of a Formal Deduc- 
tive Science. 

The processes of Deduction are seen to advantage in Mathe- 
matics. The Definitions, Axioms, Demonstrations, Symbolical 
language, and various devices for multiplying the relations of 
quantity, the subject-matter of the science, exhibit all the 
machinery for performing Deductive operations of a Formal 
nature. 

2. Mathematics treats of Quantity in the Abstract, so 
far as susceptible of definite expression. 

The first, the deepest, the most fundamental experieno 
the human mind is Relation, or Relativity ; tin- ifl unplic 
in the very nature of consciousness. The clou oh i 
essential two-sidedness of every conscious experience is a 
that has no forerunner. OH the differences, contrasts, or 
relative couples, starting immediately from this prii 
condition, the first is difference in Quantity or Degree — the 
distinction of more and les3. 



430 LOGIC OF MATHEMATICS. 

Quantity adheres both to subject and to object, but it is not 
always definite ; and none but definite expressions enter into 
Mathematics. The most definite form of quantity is Number, 
or discrete quantity— one, two, three, &c. Continuous or 
unbroken quantity is made definite chiefly by its being broken 
artificially and made numerical. In a few instances, as in the 
geometry of Incommensurables, definite relations can be ex- 
pressed by lines in figures ; such is the relation of the side to 
the diagonal of a square. A difliculty of a metaphysical nature 
has long attended the mathematical expression of continuous 
quantity in these incommensurable relations. 

Notions of Mathematics, 

3. An enumeration of the principal Notions occurring 
in Mathematics, prepares us for ascertaining the character 
of the propositions. 

The chief notion is Equality, with its opposite Inequality. 
This is the prevailing predicate in Mathematics. Likeness 
(implicating unlikeness) applied to amount or degree gives 
Equality. There may be likeness in other properties, as sound, 
colour, pleasure ; but, except in quantity, there cannot be 
Equality. We can both discriminate and classify, apart from 
Mathematics, but when we declare things equal or unequal, 
we are announcing propositions purely mathematical. 

In detecting equality, the final appeal is to sense or con- 
sciousness. For Number, we identify a succession of beats, 
or remitted impressions, as two, or three ; this is the surest 
judgment that the human mind can form. For Continuous 
Quantity, we discriminate grades of continuance by the sense 
proper to the peculiar effect— the eye, the ear, the touch, &c. : 
the most delicate discrimination, and the one that, if possible, 
all others are reduced to, is visible extension ; next in rank 
is the continuance of sound. Euclid's definition of Equality is 
the visible coincidence of extended magnitudes. 

Number is thus seen to be a fundamental notion of Mathe- 
matics, as the science of Quantity. Interrupted sensations, 
or transitions, of consciousness, are vividly discriminated ; and 
by memory we can easily retain a small succession of these, 
and identify it with another small succession. Thus, three 
coins seen by the eye, are identified to a certainty, with the 
three fingers, in respect of the number of interruptions or 
transitions ; they are felt to be different from two or from four 
visible transitions. This is numerical equality or inequality. 



I NOTIONS OF MATIIKMATl 

For the higher numbers, artificial aids are requi 
eorfcainty of comparison ; bub with such aids (uaraerj 
groupings) we can compare numbers of any amount 
can identity one hundred in two different a 
number, and discriminate one hundred from ninety-nine. 

Names are given to the successive numbers, one, two, thre >, 
four, five, &c. ; at the number ten, a group is form ■ I, an 
start afresh. ^ This is our decimal system., to win 
the designations units, tens, hundred*, &c. 

Addition is the next fundamental notion; al 
in the last resort, from the senses. When we br 
detached groups or successions from different plac 
same place, or into one continuous group or succession, we 
are said to add; the implicated contrary is to Subtract. 
names ivliole and part refer to the same operation, and ar 
plained by the same experience. Multiplication is merely a 
continued addition, and its obverse is Division. These; notions 
are the names of the four cardinal processes of the manipula- 
tion of numbers. Related to them are the meanings of sum, 
difference, remainder, factor, product, dividend, divisor, qu >- 
tient, prime number. 

Fraction (versus Integer) grows out of division ; also the 
designations numerator and denominator, common 
To fractions are applied the cardinal operations — addition, &c. 

Decimal is a fractional mode, related to our decimal enu- 
meration. 

Square, cube, square root, cube root, &c, are special growths 
or extensions of multiplication and division respectively. 

Eatio is the statement or implication of how many times one 
number is contained in another; the ratio of three to twelve 
is four, or one to four. We do not always reduce the ratio to 
the lowest terms; we may speak of the ratio of three to six, 
but the comparison of the numbers is by multiplication or divi- 
sion. The expression of ratios takes the form of fractions. 

Proportion is equality cf ratios ; three is to eight in the pro- 
portion of nine to twenty-four. 

Ratio, Proportion, and Fraction, conduct us to t!, 
Incommensurable. 

Progression, or series, is a succession of numb 
to a fixed law; the Arithmetical progression b 
by addition, the Geometrical, by multiplication. A 
contains Extremes and Means. 

Permutations and Combinations are modes of operating upon 
numbers that need not here be explained. 



432 LOGIC OF MATHEMATICS. 

Logarithm signifies a still more advanced notion ; being the 
name for an entirely novel mode of expressing the relations of 
numbers, which, when unfolded in tables, greatly reduces 
the labour of the higher operations, namely, multiplication, 
division, raising to powers and extraction of roots. 

The foregoing comprise the leading notions of mathematics 
for the initial branch, called pure Arithmetic. For Concrete 
or commercial Arithmetic, there are involved farther the money | 
standards, the weights and measures, together with the adapta- 
tion of the cardinal processes of proportion and of fractions, to 
compute these several varieties of concrete quantity. 

Algebra carries forward all the arithmetical notions to a 
new order of expressions of quantity. The detaching of the 
operations from the actual numbers, by the use of symbols, 
gives new designations, Negative Quantify, Index, Exponent, 
Surd, Impossible Quantities. The general theorem for expand- ! 
ing by powers or roots is the Binomial Theorem. Then follows 
the liquation — Simple, Quadratic, &c. 

The Notions of Geometry are comprised in the Definitions 
of Euclid : — Point, line, straight line, curve line, angle, paral- 
lels, surface, solid, triangle, quadrangle, polygon, circle, cube, 
sphere, cylinder, cone, &c. 

In Trigonometry there are new designations — sine, co-sine, 
tangent, secant. 

In Conic Sections are comprised the figures so named with 
the further designations — eccentricity, focus, directrix, latus ' 
rectum, parameter, abscissa, normal, asymptote. 
^ Analytical Geometry involves co-ordinates and loci ; and ds- 
signates a number of curves reserved for analytical handling — 
cissoid, conchoid, witch, lemniscata, catenary, cycloid, invo- 
lutes, spirals, &c. 
_ The higher Calculus introduces us to the notions— Infinite- 
simal, Differential, Integral, Limit, Dependent and Independent, 
Variable. 

Propositions of Mathematics. 

4. In the logical aspect, these propositions are leading 
examples of the predicable, called proprium. The predi- 
cate is deducible and demonstrable from the subject. 

The Axioms are inductions of concomitant properties. In 
all other propositions (excepting those that are in reality defini- 
tions), the predicate is deducible from the subject through the 
axioms. Thus, in the simple Arithmetical proposition, six 



DEFINITIONS OF ARITHMETIC. 

times four is twenty four, the predicate (2 i) follows from 

eubject (6 times 4) by the medium of the t* 

equality. Tiie predicates are not contained in the Bubjec 

necessary or immediate implication ; they are medi 

ences drawn by the help of the highest generaliti mpli- 

fying the true nature of the propriunu 

Definition in Mathematics. 
5. Certain of the Notions of Mathematics are fm, 
mental and indefinable ; the rest are defined by derivation 
or Analysis. 

It will be sufficient to advert to the specialities conneeted 
with (1) Arithmetic, and (2) Geometry. 

Definitions of Arithmetic.— Vfe have" seen that Number or 
discrete quantity, is a series of intermitted impressions on the 
mind — patches of colour, sounds, &c. This is an ultimate fact ; 
language can give no account of it in any other way than by 
calling each one's attention to their own experience, 
regards the numbers themselves, experience must give as a 
few to begin with ; the rest may be derived and defined from 
these. Unity is an ultimate reference, the abstraction from 
numerous concrete objects, that is, from many single impres- 
sions ; it is contrasted with two, and with the higher succes- 
sions. We learn one, two, three, four, five, &c, by repeated 
experiences of the successions so named; the hand is a 
familiar example of five. We might go a good way in dis- 
tinguishing the successive numbers; but, in point of fact, 
when a dozen or thereby is reached, we resort to modes of 
comparison that imply grouped arrangements. 

So much for our actual experience of numbers, which is 
presupposed in the attempt to define them. For the actual 
purposes of a strict definition, we must assume one as indeu li- 
able, that is, as already known. Even this supposes that we 
know tzvo at least, for, without a contrast with plurality, we 
cannot possess the meaning of unity. 

Before going farther, it is necessary to suppose that 
understand addition. This is an abstract notion gained from 
many concrete experiences of accumulating objects in D 
We cannot define it; we must point to the operation: 
operation, as already remarked, that makes known tubtractitm, 
likewise ; and also whole and part. To attempt to define 
of these notions is to encroach upon the ultimate expert 
of the mind ; and the futility is shown by the words employed, 



431 LOGIC OF MATHEMATICS. 

4 aggregation/ &c, which are not more elementary, or more 
simple, than the notions that they are used to define. 

With a knowledge of one, and of addition, we may begin to 
define. The lowest definable number is then two ; we may 
define it by the addition of one and one. The rest follow : 
three is two added to one ; four is three and one ; five is four 
and one, and so on. Each number is definable as one added 
to the previous number. Arriving at ten, we bring into play 
the decimal notation, or the grouping by tens, which gives us 
double expressions : eleven is ten and one ; twelve is eleven 
and one, and also ten and two ; fifteen is fourteen and one, and 
also ten and five. We may be supposed at this stage to make 
use chiefly of the second form, although always aware of its 
equivalence to the first ; sixteen is ten and six ; twenty-seven 
is twenty (two tens) and seven. 

All the other notions of Arithmetic are susceptible of defini- 
tion properly so called ; they may be derived from the notions 
now given. In logical strictness, there is no need for a farther 
appeal to experience ; although the actual understanding of 
the processes is aided by using concrete examples of numbers 
and their formations. 

Definitions of Geometry. — The difficulties here are far more 
serious ; yet the proceeding is the same. We must recognize 
a certain basis of the indefinable, a resort to experience for 
what can be given only by experience. 

By experience, we become familiar with all the modes of 
extension, and learn the names for them. We know solid 
bulk, surface or area, length, angle, direction, straight, bent, 
curved, parallel, and so on. We also know what a Point is, 
in the peculiar acceptation of a landmark, or a place to measure 
from, to begin, to terminate, or to divide a length. While 
Solid Balk is the one concrete fact, all the rest are abstractions, 
and we learn to understand them in that character. We can 
consider a line, or length, without affirming anything of the 
breadth of the thing discussed ; we can restrict our affirma- 
tions to what would be true under any width, as when we 
say a piece of string and a plank are of equal lengths. By a 
large concrete experience of this nature, we are prepared for 
the more rigorous methods of arranging and stating thsse 
notions in Geometry. 

To advert more particularly to our experience of Lines or 
lengths, abstraction being made of the accompanying breadth 
and thickness. In this one experience is wrapt up inextricably 
a whole group of the notions given by the geometer in separa- 



DEFINITIONS OF aBOMETl 

tion. In working with rods, with strings, with \\ 

other things, we learn, not only length (as greater or less), bat 

bJso tho difference between straight and bent, orooked <»r 

curved; together with direction, angles, and parallel 
Straightness, direction, angle, convergence, dii 
parallelism, however separated in Geomel 
mingled in our primitive concrete experience; and, iu 
any one would be incompletely understood it' it did not involft 
all the rest. We cannot understand the fall force of ' 
ness' without understanding what is meant by direc 
'direction* would be very incomplete without involving the 
meaning of an angle ; and the concrete experience of an i 
gives all that is meant by convergence and divergence, and 
also by the opposite of these — parallelism. 

All these notions, therefore, have to be assumed as being 
perfectly intelligible and as wholly indefinable. We cm 
assign nothing more simple or more elementary to define 
them by. The attempt to define an 'angle' only returns 
upon itself; thus, an angle is said to be the inclination q) 
lines, but 'inclination' is merely another name for angle 
well say, 'an angle is an angle.'* 

Geometry, as well as Arithmetic, is a Deductive Science. 
Now it is the idea of a deductive science to assume the fe 
notions possible, and to begin to define, or derive, as soon as 
there has been laid an adequate foundation in the indefinable. 

To make the application to the case in hand. The fewest 
elementary notions that we can proceed with may be differ- 
ently stated by different persons ; but one cannot be far w 
in the following : — point or landmark, line or length, straight, 
as contrasted with bent, angle, surface, solid. The three — 
line, straightness, angle — are really phases of one experience ; 
and, by a great stretch of ingenuity, we might find i 
to condense the three expressions into two, or even into one; 
for undoubtedly the line (as carrying with it length) impl 

* 'Geometrical definitions are of thrte kinds : (1) 
our primary ideas of space, such as the definitions of a straight i 
angle, a plane, &c. (2) Those which by means of the 6 define 

certain simple forms, the triangle, the square, and the circle, 
properties of which all calculation of relative positions and sap i 

magnitudes is derived. (3) Definitions of other forms, as tho rhombtt*, 
trapezium, hexagon, ellipse, &c, the properties of which are found b 
application of theorems obtain* d from the definitions o. th 
(Challis on Calculation, p. 61). 

'lhe last named class exemplify what are called Deductive I 
(p. 165). 



436 LOGIC OF MATHEMATICS. 

'straightness/ which itself involves its opposite lending, 5 
and also ' direction ;' and from direction we cannot separate 
change or variety of direction, as exhibited in an ' angle/ Not- 
withstanding this inevitable mntnal implication, we may- 
retain the above enumeration of primary or indefinable notions 
— point, line or length, straight (with bent), angle, surface, solid 
(it would be a vain refinement to treat * surface ; and * solid ! 
as derived from length, or vice versa). From these we are 
able, by proper analytic definition, to give an account of ail 
the other geometrical notions. It is requisite, however, to 
unfold the immediate implications of each, and to state which 
phase, aspect, or property shall be put forward, in the subse- 
quent demonstrations, as the testing property. 

Point. — As stated, this is the same meaning as landmark ; 
for geometric purposes, we hold it as the beginning, division, 
or end, of length or a line ; all which must be understood by 
actual experience. 

Line or length. — It is impossible to give a definite meaning 
to ' line ' without at once distinguishing the straight from the 
bent line ; it is only the straight line that is synonymous with 
4 length.' The mutually implicated notions — length and 
straightness — are absolutely incommunicable by any device of 
language; they cannot even be made clearer by discussion. 
We may, however, select one feature or aspect as the test to be 
referred to in the course of the demonstrations, namely, that 
* two straight lines, if made to coincide in two points, will 
coincide wholly/ will have no interval ; all which ideas the 
learner has to bring with him from his own independent 
experience. Another aspect of the straight line, sometimes 
given as its definition, is * the shortest distance between two 
points ;' this, however, may be proved by proper demonstra- 
tion ; being a corollary to the proposition that two sides of a 
triangle are greater than the third. At the same time, it is 
sufficiently implicated w r ith our experience of lines to be 
received without proof. 

Angle. — This also must be known from experience. We 
must see with our eyes two straight objects meeting with a 
greater or less opening. That experience supplements our 
education in ' direction,' and gives us what is meant by 
' divergence ' and ' convergence,' greater or less. There is a 
farther implication of two lines running side by side, and 
neither diverging nor converging ; to this fact we give the 
designations ' sameness of direction and parallelism ; ' all 
incommunicable notions. 



FUNDAMENTAL NOTIONS OF QSQMSTBT. 

It may then he formally proper to describe an angl 
straigkt lines meeting in a point, with greater or li 
gence. This is merely one way of referring as to our 
ence of the fact; and it is thought the best workabl 
an angle in the subsequent references. 

With the angle, we can conveniently connect the notion of 
1 Direction.' Inasmuch as all direction is relativ 
be two lines given, and the angle they end. 
parison of the two directions. Direction being nndersl 
we can define a curve line, as a perpetually changing d 
tion ; which is an obverse equivalent of Euclid's phra 
of which no part is straight; ' both expressions being pi 
to be retained. 

Parallels.— These are inevitably understood along with 
notions already given. As to their formal, or test definition, 
Euclid's original expression, 'two lines in the same piano. 
duced ever so far both ways, and yet not meeting,' is properly 
% negation of both convergence and divergence, and is 
ciently workable, which is all that need be said for any defi- 
nition. 

Plane Surface. — This is clearly an incommunicable notion. 
It would be superfluous to construct it by the help of lines, for, 
while we are learning lines, we are also learning sun 
All that is needed is a convenient testing peculiarity, such as 
that given by Euclid, — ' any two points being taken in a 
plane, the straight line joining them lies wholly within the 
plane.' The notions ' within ' and * without ' must be got 
from our manifold experience of extended bodies. 

Solid Bulk. — Also incommunicable by any simpler notions. 
If we seem to define it by combining the notions of * pianos ' 
'directions,' &c, we in reality repeat ourselves ; for these 
notions were attained by a mass of experiences including 
solid bulk or volume. 

The elementary notions now enumerated being once obtained 
from experience, the remaining notions of geometry arc defin- 
able by referring to these. No new appeal to the 
absolutely required in defining a right angle, a circle, a triangle, 
a square ; although we are constantly aided by concrete re- 
presentations in understanding these notions. 

Axioms of M cithern" 

6. The Axioms of Mathematics should conform to the 
conditions of an axiom, namely, (1) they should 



438 LOGIC OF MATHEMATICS. 

propositions, and (2) they should be underivable from any 
other principles within the science. 

An axiom is, in the first place, a real proposition, and not a 
verbid or essential proposition. The axioms are the ground- 
work of all the reasonings in the science, but no reasoning 
can be based on merely verbal propositions. 

In the next place, the axiom should be absolutely funda- 
mental and underivable within its own science. All that is 
characteristic of the axiom is surrendered, if we admit deduced 
principles. The axioms are the undeducible grounds of all 
the deductions. 

It is not a proper account of an axiom to say that it is a 
self -evident proposition, or a proposition assented to as soon as 
pronounced. This may or may not be the care. Some axioms 
are self evident, others not ; and many principles that are 
self-evident are not to be received as axioms. 

Axioms of Mathematics as a whole. — The axioms of Mathe- 
matics as a whole, requisite to be given at the threshold of 
Arithmetic, are at least these two — ' Things equal to the same 
thing are equal to one another,' and ' The sums of equals are 
equals/ These are real propositions, inductions from experi- 
ence, and undeducible from one another. Whether they are 
sufficient for all purposes, will appear afterwards. Both are 
demanded by the processes of Arithmetic. 

Axioms of Geometry. — As it has been the practice to teach 
Arithmetic to beginners, not as a reasoned or deductive 
science, but as a series of rules given npon authority, and 
merely confirmed by their actual results, the mathematical 
axioms usually confront the learner for the first time at the 
beginning of Geometry, which from early ages has aspired 
to be, not merely a body of correct rules for measuring mag- 
nitude, but a perfect type of deductive reasoning. As thus 
presented, the axioms of all Mathematics are so mixed up 
with matters belonging to geometry in particular, as to seem 
exclusively geometrical in their bearing, These axioms, made 
familiar to us by Euclid, have to be tried by the two tests 
already laid down. 

In Euclid's original text, there occur twelve axioms (or 
common notions kuivul ty/oiai). Others have been added by 
modern editors ; it is not unusual to give fifteen. The two 
first in the enumeration are the two already mentioned as 
unquestionable axioms, conforming to both the criteria. The 
five succeeding are — 



. 



AXIOMS OF EUCLID. 



(3) If equals be taken from equals, the remain 
equal. 

(4) If equals bo added to unequals, the wholes are un- 

equal. 

(5) If from unequals, equals bo taken, the remainders aro 

unequal. 

(6) Doubles of the same are equal. 

(7) Halves of tbo same are equal. 

Now, these are all real propositions, and therefore not dis- 
qualified by the first condition ; but as they are all very easily 
dedacible from the two first, they fail to comply with the 
second condition. They are not axioms proper, but deduc- 
tions or corollaries from axioms, and should be demonstrated. 
If we are to call them axioms, there is nothing to prevent us 
from calling any real proposition whatever an axiom. It 
violates the very essence, the first demand, of a deductive 
science to take for granted without proof whatever can he 
proved from another principle within the science. 

The eighth axiom, ' Things that coincide, or have the same 
boundary, are equal,' violates the first test of an axiom ; it is 
not a real proposition, but a definition of equality. * Coincid- 
ing ' and ' being equal ' are not two facts but the same fact in 
two statements of language, the one being given as the expla- 
nation of the other. Equality as applied to extended magni- 
tude is coincidence to the senses ; to prove equality we prove 
coincidence. Of Equality no definition can be given in the 
last resort ; it is the feeling of similarity or identity as applied 
to quantity. But in dealing with the special kind of quantity 
considered in geometry, there is a convenience in specifying 
the test of equality belonging to the case — namely, the visible 
coincidence of the boundaries of the two things compared — 
lines or plane figures. The supposed axiom is therefore the 
geometrical statement and adaptation of the fundamental and 
indefinable notion of equality. 

The ninth axiom is 'The whole is greater than its p 
This also violates the first test ; it is not a real proposition ; 
the predicate is not different from the subject. lo is a 
perty implicated in the common fundamental notion 
gives a meaning to addition, suhtractiou, vL> /<•, part. 
concrete experience implied by all these words is one and the 
same experience, and in it is implicated the fact that whal 
call a sum is greater than any one of the amounts sum: 
up ; or what we call a luhole is greater than any of the / 
We could not possess the notion of whole and part without 



440 LOGIC OF MATHEMATICS. 

possessing the fact that the whole is a larger magnitude than 
the part.° If, therefore, there be any necessity for distinctly 
announcing this peculiar aspect of the great fundamental 
notion of "addition, it should be given as one of the forms of 
expressing the notion of Addition, when that notion is first 
introduced at the threshold of Arithmetic. 

The tenth axiom, * All right angles are equal ' is implicated 
in the definition of a right angle ; and should be stated as an \ 
appendage to that definition. 

The eleventh axiom, in Euclid's text, is a difficult theorem 
preparatory to the propositions respecting parallel lines. It 
is usually given in a modified and simpler form. Thus (by 
De Morgan) — ' If a straight line be taken, and a point 
exterior to it ; of all the straight lines that can be drawn 
through the point, one only will be parallel to the first- men- 
tioned straight line.' In whatever form given, it is not an 
axiom, but a proposition deducible from the definition of paral- 
lel lines ; in fact, it ought to appear among the Theorems of 
the first book, unless, indeed, it be so nearly identified with 
the definition of parallels that it can be given as a mere various 
wording or obvious implication of that definition ; which, 
however, is hardly the case. 

Euclid's twelfth (and last) axiom is famous in the History 
of Philosophy : 'Two straight lines cannot enclose a space/ 
It is not a real proposition, but merely an iteration of the 
very fact of straightness. The pro forma definition of this 
indefinable notion is ' When two lines cannot coincide in two 
points without coinciding altogether, they are called straight 
lines.' Now it is a synonymous variety of the expression 
1 coinciding altogether,' that there should be no intervening 
space. That the lines should be ' straight ' and that they 
should ' enclose a space ' would be a contradiction in terms. 
This axiom must, accordingly, be rejected ; the phrase * not 
enclosing a space ' being transferred to the definition of 
straightness, as an emphatic obverse iteration of ' coinciding 
altogether.' We might express it thus — ' When two lines 
cannot coincide in two points without coinciding altogether, 
that is, without excluding an intervening space, they are 
called straight lines.' 

In the modern texts of Euclid, there are added to the list of 
axioms such propositions as the following . — ' If two things be 
equal, and a third be greater than one of them, it is also 
greater than the other.' This is clearly demonstrable from 
the proper axioms, coupled with the notions of greater and less. 



POSTULATES. ' 111 

'ore notable is the argumenttim a fort im- 

ported into Logic, although in its nature strictly matb 
If A be greater than B, and B greater than C, much m 
A greater than C. Every one readily assents to this principle 
as an induction from facts of their own observing, If it c 
not be deductively inferred from the two proper axiom 
will liave to be received as a third axiom. Probably, how. 
mathematicians would be able to demonstrate it, if not directly, 
at least by reductio ad absurdum, from those axioms. 

Another example of a proposed axiom is the i ■ lowing: — 
c Of all lines that conjoin two points, there must 
none less ; if only one, that is the least.' If there is 
necessity for enunciating this circumstance, it should bo 
given as implicated in our experience of lines ; its opposil 
a contradiction in terms ; the very meaning of 'least ' is that 
there can be nothing less. 

The bringing forward of axioms at every new si age of 
Geometry is wholly at variance with the deductive character 
of the science. There may be required a class of principles, 
intermediate between the axioms proper and the demonstrated 
theorems ; but they should not be confounded with the primary 
foundations of the science ; they should have a name distinct 
from i axiom.' If inconvenience were now to arise from drop- 
ping the name in connexion vrith these preliminary princi 
some emphatic designation should be adopted for the really 
fundamental truths — 'Axioms-in-chief/ 'Axioms proper,' ' in- 
demonstrable assumptions,' ' Final Inductions.' 

The Postulates. — These are the groundwork of the construc- 
tive part of Geometry — the problems, as distinguished from 
the theorems. It is Euclid's plan to carry on, side I 
series of problems of construction and a series of theorems ; the 
constructions being required for demonstrating the theoi 
These constructions, however, have an independent vain 
practical applications; the land measurer follows En 
method in throwing out a perpendicular from the side 
field. Now, in constructing, as in demonstrating, some! 
must be assumed at the outset; and these assumption* 
to be the fewest possible. Accordingly, Euclid starts with 
demanding three operations— drawing a straight 
one point°to another, prolonging a given 
describing a circle; in concrete, he requii 
have a ruler and a pair of compass 

• 'The Postulates which are prefixed to Book I. r< |uir< 
certain geometrical operations may be performed, without res] Ct to I* 



412 LOGIC OF MATHEMATICS. 

It is averred that, in the course of Euclid's demonstrations, 
tacit assumptions are occasionally made, such as should have 
been placed among his axioms. Thus, in the fourth proposi- 
tion, there is an assumption that a figure may be lifted and 
turned upon itself without change of form. This, however, is 
part and parcel of that great step, the very earliest to be made 
in geometrical proof, whereby the comparison of two plane 
figures is achieved. As regards the first proposition, Mr. De 
Morgan points out two postulates that should have been 
explicitly given with the others ; and, for the twelfth, two 
more postulates are necessary (Companion to the British 
Almanack, for 1849). 

The leading branches of Mathematics : — Arithmetic, 
8. The foundations of Arithmetic are the two proper 
Axioms of all Mathematics, the Definitions of the funda- 
mental operations — Addition, &c, and the Definitions of 
the Numbers, The Propositions flow deductively from 
these Axioms and Definitions combined. 

The Axioms being premised, the Operations understood 
and the Numbers defined, the deduction or demonstration of 
the Propositions easily follows. 

The Propositions of Arithmetic affirm or deny the equival- 
ence in amount of numbers differently aggregated. The follow- 
ing are examples. Six and seven is equal to nine and four, 
to ten and three, &c. ; that is, a row of six and a row of seven 
would be the same total aggregate as a row of nine and a row 
of four. These are propositions of addition. As there is one 
standard mode of expressing aggregates — the decimal system, 
the arithmetical propositions usually take the form of stating 
other modes of aggregation as equivalent, or not, to a given 
decimal aggregation ; nine and five is fourteen (the decimal 
aggregate — ten and four). There are corresponding proposi- 
tions of subtraction ; nine taken from fourteen leaves five. 

manner of performing them. In fact, they appeal to our conceptions, and 
for all the purposes of reasoning might be expressed thus : 

Any two points may be conceived to be joined by a straight line. 

Any terminated straight line may be conceived to admit of unlimited 
extension. 

A circle may be supposed to have any position for its centre, and a 
radius of any magnitude. 

The following is another postulate of the same kind, which we shall 
have occasion to refer to hereafter : — 

A straight line passing through any point may be conceived to be paral- 
lel to another straight line.' (Challis on Calculation, pp. 63-4 ) 



PROOF OF THE PUOPOSITIOXS OF V 

The proof of such propositions is ti- 
Mtioms to the definitions of tho nnml 
the axioms are the major premises, the definitioi 
Thus, to prove that three and four is seven, in 
that a row of three together with a row of foui 
as a row of seven. ^Ye may proceed a 

By the definition, 3 is 2 + 1 (or again 1 -f- 1 + 1). 

Hence, 4 -f- o is the same as 4 -f- 1 + 1 4- 1. 
* i + 1, = 5 ; 5 + 1 = 6 ; and 6 + 1 -. 7. 

The warrant for these substitutions is the law 4 the sums of 
equals are equal,' applied thus : — 

1 + 1 + 1=3. 

Hence 4 + 1 + 1 + 1 (7) = 4 + 3. 

Arithmetical probation thus, at the outset, creeps along by 
a unit at a time ; when, in that way, larger leaps are e£ 
lished, the deductions are much shorter. For example, we 
can construct and commit to memory a table for the addition 
of every two mimbers up to ten (2 and 3, 2 and 4, & 

Propositions of multiplication — six times eight is forty- 
eight — are a mere extension of the process of addition. Tne 
celebrated multiplication table embodies 1-44 of these proposi- 
tions, and, by implication an equal number of propositions of 
division. 

Thus, while the affirmation ' 3 and 1 is 4,' is a verbal pro- 
position (being declaratory of the meaning of 4), * 2 it 
is four ' is a real proposition deduced from the induction ' the 
sums of equals are equal.' This last is sometimes called a 
necessary tiuth, but it is not necessary in the sense of an 
identical or implicated truth ; it is true only if the above 
axiom be true. It is sometimes called self-evident, but that 
merely means that it is very rapidly appreciated ; it 
tially of the same scientific character as 16 times 16 Is 
which would not be called self-evident. 

As there is no limit to Xumbers, so there is no limit to the 
propositions asserting (or denying) the equivalence of uu:.. 
differently stated. 

A Igebra. 

9. The vast mechanism of Algebra rests upon the funda- 
mental axioms of all Mathematics. It is 
of the compass of Arithmetic depending upon usi 
bols of numbers, and signs of operation, for actual numbers 
and actual operations. 



4J4 LOGIC OF MATHEMATICS. 

No new principles of reasoning or computation are intro- 
duced into Algebra ; its foundations are solely the axioms 
common to all mathematics. Its characteristic feature is, in 
the place of actual numbers, to employ symbols representing 
numbers generally ; and, for the actual operations of addition, 
subtraction, multiplication, division, to use signs of opera- 
tion, +, — , X, -T-, Ac. 

Numbers are no longer compared by their actual amount, 
but by their modes of formation. One number is regarded as 
made up of others formed in a particular way, shown by the 
signs of operation. A number a is given as made up of the 
sum of b and c, as b -f- c ; or of the product of b and c, as b c ; 
or of the square of b, b 2 . Oa this scheme the one number is 
said to ben, function of the others ; and the science of Algebra 
is said to be the calculus of Functions. 

The simple functions of numbers are few, being the ex- 
pression of the elementary relationships — addition, subtraction, 
multiplication, division, powers, roots, logarithms, sines. 

Mr. Challis distinguishes between Algebra and the Calculus of 
Functions. He restricts Algebra to the instrumentality and mani- 
pulating of Equations, Algebra is a more highly generalized 
scheme of symbolical expression than Arithmetic; it represents 
quantities by letters, a, b, x, y, which may have any numerical 
value, the only thing considered being their relationships to one 
another, as sums, differences, products, roots, &c. The Calculus of 
Functions is a still farther step in the same direction. It uses | 
symbols to show that one quantity has relationships to others, 
without condescending on any one form of the relationship ; / (x) 
expresses that a certain quantity is made up of some modifications 
of x, without saying what they are. It operates generally upon 
the form y =/ (tc). One leading and important enquiry is to find 
the symbolical expression, when the variable x receives a certain 
increment h, and becomes / (x -f- h). This gives birth to distinct 
theorems,called Taylor's Theorem, Maclaurin's Theorem, Lagrange's 
and Laplace's Theorems, and conducts to the Differential Calculus. 

10. Algebra shows the equivalence of different opera- 
tions ; and thereby gives the means of resolving the one 
into the other. 

This is to extend the propositions of Arithmetic. By study- 
ing the Algebraic forms, we find that the square of a sum 
(a + b) is equivalent to the squares of the separate factors 
a Ided to twice their product (a 2 -f- b 2 -|- 2 a b) ; no matter 
what the numbers are. 

1 1. The use of signs of operations readily leads to ex- 



OPERATIONS OF ALGEBRA. 

pressions not interpretable into any actual facts ; and the 

distinctive business of Algebra is to define and justify all 
its combinations. 

Subtraction in Arithmetic cannot be performed without 
something to subtract from ; the Algebraic sign — , u, 
prefixed to a number irrespective of this fact. Noi only 
the number so qualified may be formally subjec ! the 

operations performable upon real numbers. We may su] 
two negative quantities multiplied together, a proc 
be realized in fact. There is a still greater departure from 
possibility in placing a negative quantity under the Bigi 
extracting the square root, V — 1, V ■ — a. 

It is necessary to qualify the rules for the cardinal O] 
tions of Arithmetic, in their extension to Algebraic quantities, 
by explaining the conditions of the use of the signs : — to lay 
down and demonstrate such rules as ' minus multiplied In- 
plus gives minus;' 'minus multiplied by minus gives plus/ 
Although the demonstration of such rules is a matter for 
logical discussion, we do not enter upon it here. Mathe- 
maticians usually satisfy themselves in all such cases I 
appeal to the verification of experience ; to which they append 
some form of deductive proof. But deductive proofs in such 
matters would never be trusted by themselves, or in the 
absence of verifications. Thus, ' minus multiplied by minus 
makes plus/ is shown by manipulating the product of two 
differences as a — b, by c — d ; where it is seen that ouly by 
this rule can we obtain a correct result. 

12. The highest form of the Algebraical problem is the 
Resolution of Equations. 

This contains all the preceding processes, and applies them 
in an advantageous manner to disentangle complicated relation- 
ships of numbers. 

In an Equation, two expressions known to be equal are 
placed against one another ; as — 

13 x + 2 a — b = 6 x — c. 
By applying the fundamental axioms of equality, and a f 
the convenient derivatives from them (the differe i [nah 

are equal, equal multiples and equal quotients i 
equal, the squares, square roots, &c, of equals ai 
equation may be so manipulated that there may staml, at 
on one side, the quantity x (whose value is desii 
the other, a function made up of a, b } c, to the exclusion t 



4i6 LOGIC OF MATHEMATICS. 

strict equality being preserved at every step of the transform- 
ing operation. No logical difficulties are involved in this 
rehned and powerful machinery ; while it may be quoted as 
happily exemplifying the intervention of the axioms and 
derivative propositions of equality. 

Geometry. 

13. Some of the more difficult logical questions arising 
out of Geometry — those relating to the Definitions, Axioms, 
and Postulates — have been already considered ; it remains 
to advert to the order of topics. 

Every science reposes alike on Definitions and on Axioms ; 
which accordingly are stated at the outset. Generally speak- 
ing, the Definitions come first, the Axioms next. But the 
Axioms of Geometry may be supposed already given, as the 
indispensible basis of Arithmetic, and, therefore, need only to 
be recited along with any corollaries or derivatives especially 
required in Geometry. 

It would be advisable to state first of all the concrete basis . 
of Geometry — to give the notions attainable only from concrete 
experience. These have been already enumerated. To make 
a broad separation between these ultimate indefinable notions, 
and the properly definable, the expositor might interpose the 
review of the Axioms, especially dwelling upon their inductive 
character, and drawing the line between the fundamental and 
the derivative. At this stage the teacher should allow himself 
the fullest latitude of concrete illustration. 

Next would follow the remaining Definitions in order of 
derivation or dependence. Frequently, corollaries are given 
also ; but these are not proper, or mediate, inferences ; they 
are mere equivalents of the definition, not to be denied with- 
out self-contradiction. Such are, ' only one straight line can 
be drawn between two points ; ' 'all right angles are equal.' 
No mediate inference can be drawn from a Definition without 
the introduction of an axiom ; a truly deductive process, 
amounting to a theorem. 

Euclid's three first propositions are problems or construc- 
tions. The first theorem is the real start of the Geometrical 
concatenation ; namely, the fourth proposition — establishing 
the equality throughout of the two triangles having two sides 
and the included angle equal. This is the sole basis of geo- 
metrical comparison, the commencing stride that renders pos- 
sible all the subsequent assertions as to the equality and 



EUCLID'S FOURTH PROPOSITION. | | 7 

inequality of triangles, parallelograms, &c. The proof of the 
proposition is peculiar; only onco again (I. 8) is the Bame opera- 
tiou made use of ; namely, the ideal placing of the one triangle 
upon the other. Here, in fact, we have an inevitable ai 
to experiment or trial in the concrete ; just as in the d< 
tions and the axioms, we must take our first lessons from the 
manipulation of actual objects. Euclid, by his mod 
ing the demonstration, professedly goes through a p 
pure deduction, all the time that he requires us to conceiv 
experimental proof. He appears to be using merely an illus- 
tration in the concrete ; but if his readers had not made ac 1T >^ 
experiments of the kind indicated, (doubtless the same ex- 
periments as gave the original notions of line, angle and sur- 
face) they could not be convinced by the reasoning in the de- 
monstration. 

If apparently a proposition be proved without appealing 
to an axiom (either directly or indirectly), shows that the 
proposition cannot be real ; the subject and predicate must 
be identical. The proof rests solely on definitions ; but a 
definition by itself cannot advance us a step. The propo- 
sition must, in fact, be a mere equivalent of the notions of 
line, angle, surface, equality — a fact apparent in the operation 
of understanding these notions. It is implicated in the experi- 
ence requisite for mastering the indefinable elements of Geo- 
metry : and should be rested purely on the basis of experience.* 

The 5th proposition is what really constitutes Euclid's first 
demonstration by a genuine process of reasoning. In it, there 
is a legitimate deduction from the axioms common to all 
mathematics, conjoined w T ith the induction, falsely called a 
iemonstration, given as the 4th proposition. The axioms 
ipplied are, the proper axiom, 'the sums of equals are equal,' 
ind the derivative, ' the differences of equals are equal.' 

14. It is the characteristic of elementary Geometry to 
Maintain the concrete reference to diagrams, which gives 
lie subject to appearance, but only to appearance, an 
nductive or experimental character. 

* Mr. Challts remarks, on the Fourth Proposition, that tho proof 1 
n no previous proposition, and appeals only to the simplest C 
f space. 'This proposition is proved by the principle of super? > 
.either requiring, nor admitting of, any other direct pi 
bservation of Mr. De Morgan's is well exemplify <1 by Euclid 1 ! atl 
demonstrate this fundamental assumption-— 4 Haw Conversion ot identity 
•y help of a syllogism is reasoning in a circle.* 
20 



448 LOGIC OF MATHEMATICS. 

All symbolical reasonings are liable to mistake. Not to 
Bpcak of the slips that the reasoner himself may commit 
unknowingly, there is often a failure of adaptation between 
the laws of the symbols and the laws of the matter they are 
applied to. For this the remedy is the constant verifica- 
tion of the results. Now, in Geometry, an actual figure is 
always before the eyes, and the effect of every construction 
and every step of reasoning is judged of by actual inspection. 
When the direction is given to join the opposite angles of a 
quadrilateral, there is apparent to the glance the division of 
f ~ figure into two triangles. For the most part, Euclid offers 
no other proof of this class of consequences. Sometimes he 
applies the redudio ad absurdum in such cases, as in the proof 
that the tangent to a circle falls without the circle. 

So long as Geometry is discussed in the concrete, or by 
naming lines, angles, circles, the mind must conceive them in 
the concrete, which would be impracticable without the help 
of diagrams. In Algebraic Geometry, the concrete form is 
exchanged for numerical equivalents, to be manipulated accord- 
ing to the laws of operation in Arithmetic or Algebra; a 
rectangle is no longer a fact of space but a product of numbers 
or symbols ; a curve is an equation. The student is cautioned 
by Mr. De Morgan that, although the names ' square ' and 
4 cube < are transferred to Algebraic quantities, as a 2 , a 3 , the 
names mean different things from geometrical squares and 
cubes. 

Algebraic Geometry. 

15. The expression of Geometrical quantities by Algebra, \ 
while depriving the mind of the assistance of the diagrams, 
greatly enlarges the power of demonstration and inference. 

Compare Euclid's 2nd book with the same propositions 
algebraically rendered ; the one is laborious, the other com- 
paratively easy. 

The great device of Descartes, for expressing curves alge- 
braically by co-ordinates whose relation in each case could be 
stated in a formula, opened up a new field of mathematics. 
The conic sections became comparatively easy ; and curves of 
a still higher order that would have baffled common geometry 
were brought under investigation. The method was also an 
essential prelude to the Differential calculus. 

16. Algebraic Geometry furnishes specific rules for the 
embodiment and for the interpretation of formulae. The 
rest is pure algebra. 



INCOMMENSURABLE^ 



I I 'J 



It is easy to embody a rectangle, in terms of tibe si«l, 
algebraic product is sufficient for the purpose. Angles may 
be expressed by their proportion to the circle, that is by their 
subtended arc, and also by their sines, tangents, irvea 

are given by co-ordinates on the Cartesian plan. The rules of 
embodiment are also the rules of interpretation. But as there 
is frequent danger of overstepping geometrical condition by 
algebraical operations, the interpretation must be continually 
verified. Mathematics is the slipperiest of sciences ; its ana- 
lytical processes are full of pitfalls; but luckily, it is the easiest 
to keep right by verification. The arithmetical symbols 1 1 
1 are used with a latitude that makes them ambiguous, d i 
for each case, there is a distinct understanding made and ad- 
hered to. 

The Higher Calculus. 

] 7. The representation of continuous quantity, by means 
of numbers, in certain cases, fails to give a neat or "definite 
result. 

Continuous quantity, as exemplified in lines and in motions, 
must be supposed to be broken up into equal portions in order 
to be expressed numerically, and thereby to be made the 
subject of arithmetical computation. In certain instances, the 
division cannot be made without a remainder* Hence arises 
a peculiar difficulty. 

In vulgar fractions, first emerges the peculiar case of incom- 
mensurable quantities, that is, quantities that have no common 
measure. In Geometry, the side and diagonal of a square are 
incommensurable ; if the side be divided into equal divisions, 
no matter how many, these divisions will not apply to the 
diagonal without a remainder. So with the diameter and the 
circumference of a circle. 

18. The solution of Incommensurables, and the acom- 
modation of numbers to continuous quantities generally, 
can only be approximate. A variety of modes have been 
Revised, at bottom the same, for working out the approxi- 
mation. 

Mathematicians long struggled to evade the difficulty before 
acknowledging the true character of the solution. A great 
number of persons refused to believe that the diameter and 
circumference of a circle would for ever remain incommensur- 
able. 



450 LOGIC OF MATHEMATICS. 

Euclid's definition of proportionals is deservedly admired 
for its ingenuity in endeavouring to comprise incommensurable 
quantities; but it is not satisfactory. A competent judge 
(De Morgan) remarks, first, the want of obvious connexion 
between it and the ordinary well-established ideas of propor- 
tion ; secondly, its involving an idea of infinity; and lastly, 
the apparent unlikelihood that any quantities exist capable of 
satisfying the definition. The difficulties can be met only by 
the method of approximation, on which is based the whole 
structure of the higher or transcendental analysis. 

The first application of the approximate methods was to the 
quadrature of the circle, as given in Euclid. The process 
there given is commonly called the method of Exhaustions. 
The gist of the matter lies in the proposition — c A circle being 
given, two similar polygons may be found, the one described 
about the circle the other inscribed within it, such as shall 
differ by a space less than any given space*' These last words 
give the idea running through all the processes, named the 
Theory of Limits, Prime and Ultimate Ratios, Infinitesimal 
Quantities. A curve line can never be a straight line, but by 
diminishing the arc, the approximation of the two increases, 
until at last we pass not only beyond any sensible error, but 
beyond any error that may be assigned. Thus an arc may be 
said to be the limit of its chord ; the area of a circle may be 
said to be identical with an inscribed, or a described, polygon 
of an infinite number of sides. Now as the polygon consists 
of a series of triangles with a common apex in the centre, the 
area of the polygon is equal to half the product of the radius 
and the sum of the bases, or chords : and by diminishing these 
chords without limit, they become identical with the circum- 
ference of the circle. 

The method of Exhaustions was applied by Archimedes to 
the quadrature of the parabola, and to the solid measurement 
of the cone, sphere, and cylinder ; all which give neat solutions, 
or expressions in finite terms. The subsequent developments 
were left for modern times, after the discovery of algebra ; and 
they advanced as algebra and its applications to geometry 
advanced. The Fluxions of Newton and the Differential Cal- 
culus of Leibnitz were the great algebraic embodiments. 
These methods contained a new order of quantities, called 
Fluxions (by Newton) and Differential Co-efficients (by Leib- 
nitz), formed from ordinary quantities on considerations grow- 
ing out of the method of Limits, and resolved back again on 
the same laws. The quantities once created, the operations 



TWO DEPARTMENTS OF PIIYSIC3. .{ ;, | 

were treated as pure algebra, and mathematicians left them to 
be justified by their results, rarely attempting to render a 
son for the assumptions lurking uuder them. Henc 
attacks upon the system as Berkeley's famous 
the tiaxioual calculus operated upon the ghosts of 
quantities. The neglect to assign the true basis of bne cal- 
culus, and the treating it from hrst to last as a pure algebraic 
assumption, culminated in Lagrange; agaiust whom VVn 
and De Morgan have reclaimed, and have provided the n 
sarv reconciliation of the algebra with the conditions of the 
various problems to be solved ; showing that approximation 
and compromise must be held as essential to the operation. 



CHAPTER IL 

LOGIC OF PHYSICS. 

1. It has been seen (Introduction) that the branch of 
science termed Natural Philosophy or Physics is divided 
into two parts — Molar Physics and Molecular Physics. 

The aggregate called Natural Philosophy scarcely admits of 
definition, until separated into distinct departments — Molar 
Physics, or Motion in Mass, and Molecular Physics, or Motion 
in Molecule. 

The Physics of Masses, Molar Physics, includes the pheno- 
mena of Motion and Force, as belonging to bodies in the 
aggregate. Such are the phenomena of plauetary motions, of 
falling bodies, rivers, winds, &e. 

The Physics of Molecules, Molecular Physics, relates to the 
motions and forces operating between particles or molecules, 
these being of a degree of minuteness far beyond the re i 
the human senses. The phenomena representing such no 
and forces, are the Aggregations into masses ; Uohes 
Adhesions generally ; Heat; Electricity; Light. 
tion is made of the peculiar form of molecular foro 
Chemical force, as having a character and confluences 
peculiar to itself. 



452 LOGIC OF PHYSICS. 

MOLAR PHYSICS. 
Divisions of the Subject. 

2. The Abstract Branches, comprising Motion and 
Force in general, and susceptible of Deductive and Mathe- 
matical treatment are these : — 

Mathematics of Motion — Kinematics. 
Forces (1) in Equilibrio — Statics. 
Forces (2) causing Motion — Dynamics. 

The Concrete Branches are — 

Mecfianic Powers and Solid Machinery. 
Hydrostatics and Hydro-dynamics. 
Aerostatics and Pneumatics. 
Acoustics. 
Astronomy. 

Notions of Molar Physics. 

3. In Physics, are pre-supposed the Notions (as well as 
the Propositions) of Mathematics. Only those special to 
the science are here reviewed. 

Motion — Best. — This antithetic couple is the fundamental 
conception of Physics, and is probably an ultimate experience of 
the human mind. We obtain the idea of Movement by a 
peculiar employment of our active energies, assisted by sen- 
sation. We also obtain a knowledge of the varieties of move- 
ment — quick, slow, uniform, varying, straight, curved, con- 
tinuous, reciprocating, pendulous, wave-like, &c. The 
xiiodes that depend upon degree, or Velocity, are part of the 
ultimate experience of motion as such ; those characterized by 
shape or Form have a property common to mere extension. 

force. — This is without doubt the most fundamental notion 
of the human mind ; in the order of evolution, it concurs with, 
if it is not prior to, both motion and extension. It cannot be 
defined except in the mode peculiar to ultimate notions. The 
feeling that we have when we expend muscular energy, in 
resisting or in causing movement, is unique and irresolvable. 

Inertia, Resistance, Momentum. — These names designate our 
experience of force from the objective side, or as embodied in 
the things of the object world. The occasion of calling forth 
our feeling of energy when referred to an external fact is Re- 
sistance, Inertness, Momentum, or External Force — all signi- 



NOTIONS OF MOLAR PHYSICS. 

fying the same thing. This great fact must be learnt, in tho 
first instance, by each one's separate experience ; the best mode 
of scientifically expressing it is a mutter for di. 

Matter is Extension, coupled with Farce or / Any. 

thing extended and at the same time possessing force, either 
to resist or to impart motion is Material. 

Mass, Density, Solidity, are derived notions ; they are oh- 
tained by putting together Force and Extension or Volume, 
The Mass is the collective Force of a body, shown by its deg] 
of Resistance, and also by the amount of Resistance it°can 
overcome when moving at a given rate. The Density is tho 
degree of space concentration ; a given power of resistance, 
with a smaller bulk or volume, is a greater Density. Solidity, 
when not signifying the solid state of matter generally, 
opposed to liquid or gas, is another name for Density. 

Impact is a phenomenon expressed by means of Space or 
Extension, Motion, and Force. It is one mode of imparting 
visible or kinetic energy, and is a test or measure of Force. 

Attraction is definable by Extension, Motion, and Force. 
It is a mode of communicating Force, distinct from Impact, 
and in some respects simpler. Among its specific examples 
are Gravity, Cohesion, Adhesion. Magnetism, Electrical Attrac- 
tion, (Chemical Attraction). 

Repulsion is definable by reference to the same fundamental 
notions. It also is a mode of imparting or redistributing 
force, and differs from Attraction only in the way that it 
changes the relative situation of the masses concerned. It is 
exemplified in the Expansive energy of Gases in their ordinary 
state, in the Expansion of Liquids and Solids from rise of 
temperature and after compression (called Elasticity). The 
Polar Forces — Magnetism, Electricity, &c, exercise, along with 
Attraction, a counterpart Repulsion. 

By still farther combining these primary notions, we obtain 
— Equilibrium, Composition and Resolution, Resultant, Virtual 
Velocity, Centripetal, Centrifugal, Tangential force, Projectile. 

To Mechanics belong Specific Gravity, Centre of Gravity, 
Stability, Oscillation, Rotation, Percussion, Friction, Mechanic 
Power, Machine, Work. 

In Hydrostatics, occur Liquid, Liquid Pressure, Liquid 
Level, Displacement, Flotation, Column of liquid.. 

In Hydro-dynamics, Liquid Motions, Eillux, Discharge, 
Liquid Waves. # 

In Aerostatics and Tneumatics, Air, Atmosphere, Expansion 
of Gases, Flow of Gases, Undulations, Atmospheric pres- 
sure. 



454 LOGIC OF PHYSICS. 

In Acoustics, Sound, Pitch, Timber, Vibrations, Noise; 
Note, Echo, Harmony. 

In Astronomy, San, Planet, Satellite, Comet, Aerolite, 
Bolid, Star, Nebula, Orbit, Ecliptic, Year, Month, Day, Eclipse, 
Transit, Parallax, Aberration, Right Ascension, Declination,; J 
Eccentricity. Node, Apside, Perihelion, Perturbation, Libration, I 
Precession, Nutation, Tides. 

Propositions of Molar Physics. 

4. These are of the following classes : — (1) The Induc- 
tions of Force and Motion ; (2) The Deductive Propria 
asserting the quantitative relationships of Motion and 
Force ; (3) Empirical laws of the concrete phenomena. 

(1) The great Inductions, commonly called the Laws of 
Motion, are the axioms of the science. These will be con- 
sidered afterwards. They are all quantitative in their expres- 
sion. Another fundamental Induction is the Law of Gravity. 

(2) The science being pre-eminently Deductive, its proposi- 
tions are for the most part deductions from the axioms. Such 
are — the propositions of the Composition and Resolution of 
Motions and Forces ; the proposition called the 'law of Areas;' 
the principle of the Mechanic Powers ; the principles of the 
pendulum ; the law of liquid pressure ; the principle that con- 
nects fluid motion with fluid support ; the laws of the propa- 
gation and the reflection of sound. 

All these matters are stated in the form of real propositions, 
which, however, may be deduced from the axioms or induc- 
tions of the science applied to the particular cases as scientifi- 
cally defined. For example, the law of fluid pressure is a 
proposition to this effect. * At any point in a fluid at rest, the 
pressure is equal in all directions ;' the subject of the proposi- 
tion supposes a fluid at rest, a point taken in it, and considera- 
tion given to the pressure ; the predicate is ' equality in all 
directions.' The proof is deductive, and ultimately rests on 
the axioms of motion and force, tagether with the definition of 
fluidity, although the proximate majors are the propositions of 
the Composition of Forces. 

Subsidiary to the working out of the science are the propo- 
sitions expressing the quantities of motion, force, &c, existing 
in actual things. Thus, besides the Law of Gravity, we have 
a statement of the numerical amount of gravity at the earth's 
surface ; also the relative gravities of different solids and 
fluids. These numerical propositions are called the data, 



I 



DEFINITION OF MOTION. 



eons'anfs, or co-efficients of tho science, and are ascertained by 
observation and experiment. 

(8) There are certain empirical laws obtained by obserra- 

tion or experiment. Such are the laws of the Strength of 

Materials (to some extent Deductive), the laws of Friction, 

the Motion of Projectiles (partly Deductive), the Plow o( 

Kivers, the Spouting of Liquids, the Compression of Liquids 

I and of Gases, the Diffusion of Sound, the action of Vibrating 

Strings, &c. These are all real propositions ; they are in their 

. nature 'propria, or deducible from ultimate principles ; but, in 

i the present state of knowledge, they must be gained by direct 

experiment. 

Definitions of Molar Phi/sics. 

5. As in Mathematics, so in Physics, there are certain 

| properties that are ultimate, and incommunicable by kn- 

| g ua S e > being known by each one's independent experi- 

I ence. Nevertheless, it is open to us to consider the best 

mode of generalizing and stating this experience. 

The facts named Motion, Force, Matter, are understood only 
by 5ur concrete experience of the things denoted by the names. 
But our crude observations may be rectified by more careful 
comparisons, and may be reduced under precise general state- 
ments. Moreover, as in Mathematics, we may select the 
aspect most suitable as a point of departure for our deductive 
reasonings. 

Definition of Motion.— Of the fact of motion no knowledge 
can be imparted; there is nothing simpler to express it by : 
'change of place ' is not more intelligible than ' motion.' Wo 
must assume that each one understands motion both gc nerically, 
and in its degrees (capable of numerical statement) ; and also 
in snch simpler modes as straight or divergent. The more 
complex movements are then definable. Velocity means degree 
of motion. The only thing needing to be expressed formally 
is the measure of Motion or Velocity with reference to Space 
and to Time; these last-named elements being presupposed 
themselves intelligible. 

Matter, Force, Inertia, These are three names for substan- 
tially the same fact. At the bottom, there is but one exp 
ence, although varied in the circumstances, namely, tho 
experience of putting forth muscular energy in causing or in 
resisting movement. To this experience we give the names 
Force and Matter, which are not two things but one thing; 



45G LOGIC OF PHYSICS. 

of winch Inertia is merely another expression. It is pure 
tautology to define one of these terms by the others ; matter is 
nothing except as giving the experience called also force ; force 
is only revealed by matter moving, or obstructing movement. 

Matter, however, affects us in other ways than by the mus- 
cular feeling of resistance or of expended energy. It is always 
extended, and in most cases visible, and also tangible. Are 
we not, then, to include these facts in the definition ? No, 
and for these reasons: — (1) Extension is not confined to 
matter ; it belongs also to empty space ; therefore, though a 
predicate of all matter, extension is not the exclusive charao, 
teristic of matter. (2) Visibility and Tangibility belong to 
many kinds of matter, but not to all matter ; hence, these 
properties cannot be the defining characters of matter in 
general, or of all matter ; they are to be reserved as properties 
of the kinds of matter wherein they occur ; solids and liquids, 
for example. Accordingly, the only fact occurring in all 
matter is the fact expressed by resistance, force, or inertia; 
all which are names for a single phenomenon. This phenome- 
non, when fully examined, and generalized to the utmost, has 
two different aspects, which we may separate in expression, bat 
cannot separate in nature ; the one is the resistance to move- 
ment by bodies, whether at rest or in motion, and the other, 
the imparting of movement or momentum by being in motion. 
The first aspect of resistance is the more popular meaning of 
inertia ; the second aspect, the imparting of movement, is the 
popular view of force ; but in the scientific consideration of 
the subject, these are but one property. 

The definition of Matter and of Inertia, or Inert substance, 
is, therefore, but one. It generalizes our familiar experiences 
of resisting motion and of communicating motion, which 
always concur in the same thing. Fully expressed, it amounts 
to the statement given in the First Law of Motion. We are 
entitled to lay down as the fundamental or defining attribute 
of matter, in whose absence matter is not, that if once at rest 
it remains at rest, and if once in motion, it continues moving 
in a straight line. To put it from rest to motion, moving 
power must be employed; to arrest its course, matter, either 
in motion or at rest, must be opposed to it. All this is 
involved in the very meaning of matter. We cannot divide 
these expressions, and assign one as the defining mark of 
matter, and the other as a predicate distinct from the defini- 
tion. No one has ever succeeded in constituting a REAL 
proposition out of these properties. The appearance of a real 



DEFINITION OF MATTER. 

proposition could be given only by assuming as the meaning of 

matter the imperfect view entertained by the 
mind (which, owing to adverse appearances and imparl 
knowledge, does not fully recognize the persistence of moi 
matter), and giving as the predicate the scientifically 
fied generalization of matter ; but when this generalization is 
attained, it is wholly embodied in the definition of matter; it 
cannot furnish one fact as a defining property and reserve 
another as a predicate. There is a definition of Inertia ; there 
is no law. 

Thus, then, the persistence in a state of rest or in a state of 
uniform rectilineal motion, is the meaning of Inertia, and of 
Matter in general ; in which meaning there is an unavoidable 
implication of active resistance, and active communication of 
motion. The difficulty is to find an expression to comprehend 
all these aspects of one indivisible property. Matter at r« 
operates at one time in dead resistance, at another time in 
using up force by itself passing into motion ; matter in motion 
may resist movement, or it may generate movement ; but, 
these are not a plurality of properties ; we cannot suppose one 
of them separated from the others. The definition employs 
plurality of phrases in order to encompass a unity. 

Matter and Inertia being thus defined by one stroke, Force 
is merely another reference to the same fact. Inert Matter in 
motion is the most characteristic expression or aspect of Force, 
and is adopted as its numerical measure ; but we cannot ex- 
clude from the idea the consideration of matter at rest. In 
measuring force by moving matter, we mean matter transferred 
from rest to motion, or from one rate of motion to a quicker ; 
this is force as generated. Again, the force is manifested in 
the abatement of the motion, in reducing bodies to the state 
of rest ; this is force as expended. 

As there is but one fact underlying Matter, Inertia, Force, 
so there is but one measure. A larger quantity of matter, or 
inertia, is the same as a larger expenditure of force to change 
the matter from rest to a given pace of motion. The ultimate 
measure is the human consciousness of expended energ 
There is a palpable impropriety in the expression, given 
law, — 4 The amount of inertia increases with the quantity of 
matter ; ' the two properties stated are but one fact. 

To sum up. Each person by their own experieuco must 
become acquainted with the concrete examples of matter and 
force. A comparison of all varieties of the phenomenon re- 
veals the presence of a common feature, at bottom one and 



458 LOGIC OF PHYSICS. 

indivisible, but variously manifested as resistance, as a source 
of movement — as persistence in rest or in uniform rectilineal 
movement. To this many-sided unity, we give the names 
Matter Inertia, Force, which have a common definition and a 
common estimate. The word Matter is the concrete name, 
while Inertia and Force are the asbtractions for what is com- 
mon to all matter. 

Mass, Density. — Mass is the quantity of matter, measured iu 
the mode already described, namely, by the expenditure re- 
quisite to change the body's state by a given amount. When 
the Mass is given, and also the volume, or bulk, we obtain the 
Density. Volume and Mass rightly precede Density, in order 
of definition. Messrs Thomson and Tait make Density pre- 
cede Mass. 

Momentum means quantity of motion ; its measure is the 
mass multiplied by the velocity. The unit quantity of 
motion is some unit of mass, multiplied by a unit of velo- 
city. Mass is usually estimated by iveight, but this is to 
anticipate the consideration of gravity, which should be ex- 
cluded from the elementary definitions of motion, matter, and 
force. 

The defining of the notions following on these — Impact, 
Attraction, Repulsion, Gravity, Cohesion, &c. — presents no 
logical difficulties. They are all derivative notions, their 
elements being the above named primary notions coupled with 
those of mathematics ; and they are defined as such, although 
concrete examples may be given to aid the understanding of 
the more difficult abstractions. 

Thus, Impact is the transfer of force from one body to 
another b} T momentary concourse ; the direction communicated 
being the direction possessed. Attraction is the continued gene- 
ration of moving force shown in the mutual approach oi two 
bodies ; Repulsion is the generation of force leading to the 
mutual recess of bodies. Gravity is the attraction inherent, 
persistent, and unchangeable in all matter, being proportioned 
to the mass, and extending to all distances, at a uniform rate of 
decrease. 

Axioms of Molar Physics. 

6. The chief axioms of the science are usually stated 
under the title— Laws of Motion. 

_ In the statement of these laws verbal and real proposi- 
tions are confounded. 




NEWTON'S LAWS OF MOTION. 

Newton's First Law— < Every body perseveres in if. 
of rest or of uniform rectilineal motion, unless compell 
change that state by impressed forces '—is merely th< 
expansion of the definition of matter, inertia, or body, i 
doubt expresses more than the vague unscientific noti 
matter, but no more than is absolutely inseparable from 
matter. It is a verbal and not a real proposition— a definition 
disguised as a proposition. 'Body ' means what Newton pro- 
dicatesof it; withdraw from 'body' all that the law affirms 
and implies, and there would be nothing left. If a body did 
not persevere in its state of rest or motion, until disturbed by 
another force, it would not possess the most elementary 
ception that we can form of body, the property of resistance. 
Of the various modes of exhausting the aspects of body, 
matter, inertia, force, it may be doubted whether Newton's 'is 
the most felicitous. At all events, the attempt would sue 
better, if the statement were in the only legitimate guise— a 
Definition. 

Newton's Second Law is—* Change of Motion is proportional 
to the impressed force, and takes place in the direction of that 
force.' This law assumes the fact of the communication or 
transfer of motion, and affirms, although not in the best 
manner, the quantitative equivalence of the motion given 
with that received. 

The Third Law is — * To every action there is always an 
equal and contrary re-action ; or the mutaal actions of any 
two bodies are always equal and oppositely directed.' More 
shortly expressed thus — ' Action and Reaction are equal and 
contrary.' Objections have often been taken to the word 
1 Re-action' in this law. The meaning put upon it by Xewton 
is gathered from his own illustrations. His examples are of 
two classes. The first puts the case of impact, as in pressing 
a body, or in drawing it by some solid medium as a cord or a 
rod. There is, to say the least, great awkwardness in repre- 
senting the communication of force by impact, in these terms : 
— 'when we push a stone with the hand, the hand is pushed 
back by the same force as the stone is moved forward ;' or 
1 a horse towing a boat is dragged backwards by the same force 
as the boat is dragged forwards.' The more natural expr. 
sion is that when one. moving body gives motion to another, 
it loses exactly the energy that it communicates; or that on 
the re-distribution of force or moving power ootbing is lost. 
Now, if there be any real affirmation in the Second Law, it \b 
this and nothing else. 



4G0 LOGIC OF PHYSICS. 

The oiber class of examples given by Newton comprises a 
distinct case, and the only case that gives the appearance of 
propriety to the word ' re-action.' It is the communication of 
movement by distinct attraction (or repulsion). When one 
body attracts a second, the second equally attracts the first; 
the attractions are mutual and equal ; the momenta produced 
are exactly the same in each. This is a fact of great import- 
ance in nature and deserves to be singled out; indeed, it is 
the only case of communicated momentum where the result is 
unaffected by disturbances that interfere with exact calcula- 
tions. 

Now this is to be regarded as a separate induction. It is 
fally consistent with the principle of the conservation of 
energy, under re-distribution, as represented by impact, 
and has some inherent probability in its favour, but still 
requires the confirmation of experience. Ingenious reasons 
might be given, why no other result should arise, but there is 
no infallible deductive cogency in applying the Law of Conser- 
vation, founded on impact, to the equality of mutual attrac- 
tions. 

Searching thus through the three Laws of Motion, we 
encounter only one principle — the principle of Conservation 
of Force under re- distribution. The second law has no mean- 
ing but this. That * change of motion is proportional to the 
impressed force ■ with difficulty escapes from being a verbal 
proposition, for there is no other measure of force but * change 
of motion,' imparted, or impartible movement. The assertion 
would have no reality but for the circumstance that a moving 
body encounters another body and changes the state of that 
other body — urging it to move or arresting its movement. 
This is a supposition not made in the bare definition of force ; 
and, therefore, we do something more than repeat the defini- 
tion, when we affirm that the force imparted to the second 
body is lost to the first. Now, this is all that the Third Law 
contains ; only that law brings into prominence the distinct 
case of force arising by attraction or repulsion at a distance. 
Discarding, therefore, the present First Law, as being but the 
definition of Inertia, we may condense the second and third 
into a single statement declaring the Conservation motive 
Energy, under re-di^tribution, whether by impact, or by 
attraction or repulsion. This is the one axiom of the Science ; 
its foundations are inductive. It is a partial statement, 
applicable to molar forces, of the all- comprehending law of the 
Conservation of Force. Indeed in the limitation to molar 



ONLY ONE LAW OF MOTION. -M [ 

force, the principle is not strictly true; it is true with re 
fco attractions and repulsions, and bonce in Astronomj 
.error is committed in applying it; it is not true of impi 
< there is always force lost in a mechanical collision, or in the 
transfer by machinery ; the lost mechanical energy re-appear- 
ing as molecular vibration or beat. 

Newton's second law has been considered as a way of pro- 
viding for the case of the communication of movement to a 
body already moving in some other direction. A force impel- 
ling in any direction will accomplish its full effect in that 
direction, even although the body should be already in motion 
in some different direction ; as when a ship sailing in a 
westerly current is propelled by a north wind. This^is the 
foundation of the law of composition of Motion and Force, but 
it is still only an application of the principle of Conservation 
of Energy under re-distribution. Direction as well as amount 
are included in the principle ; a body moving in a certain 
direction and imparting motion, imparts it in its own direc- 
tion, and in no other. Before affirming the Law of Conser- 
vation in its full generality, we are bound to verify it for this 
case as well as lor mutual attraction ; it has been verified, 
and is affirmed accordingly. 

The so-called ' Principle of Virtual Velocities ' is a hypo- 
thetical expression of the Law of Conservation suited to various 
mechanical applications, such as the demonstration of the 
mechanic powers. We cannot prove the static il proposi- 
tion of the lever, without supposing it to move. Dynamically 
the law of the mechanical powers is the only one consistent 
with the Conservation of Force ; and the dynamical proof is 
given as the statical by the supposition of a very small motion. 

7. The second great Induction of Molar Physics is the 
Law of Gravity. 

The Law of Gravity associates the two distinct properties — 
Inertia and Gravity, and declares the one to be proportioned 
to the other, throughout all varieties of matter. The L i\v is 
sufficiently expressed thus : — Every portion of matter att 
every other portion, the attraction in each being in proportion 
to the mass (or inertia), and inversely as the square of the 
distance. 

This Law has been frequently referred to, in previous parte 
of this work, as the one unequivocal case of two co-extensivo 
properties, constituting a proposition fully reciprocating, and 
convertible by simple conversion. 



462 LOGIC OF PHYSICS. 

Our unit of force (so much inerta acting through so muc 
space) is thus the unit of weight, say a pound, moved agaii 
gravity through the unit of space, say a foot. 

Concatenation and Method of Molar Physics. 

8. The branches of Molar Physics follow a Deducti 
arrangement. The Abstract departments are purely dedu 
tive ;°the Concrete unite Deduction with Experiinenta 
determinations. 

The great division into Statics and Dynamics — Equilibrium 1 
and Movement— exhausts the abstract portion of the subject, j 
These are thoroughly mathematical in their structure ; the 
propositions and demonstrations are worked out according to 
Geometry, Algebra, or the higher Calculus, respectively. ^ A i 
preliminary mathematical department is constituted, which | 
has been termed ' Kinematics,' containing propositions that 
assume only the fact of Motion, together with mathematical 
elements. The Composition and Resolution of Motions, under 
every possible variety of complication, are mathematically de- 
veloped under this branch ; it being also applicable to Optics. 
The theorems are then found to be transferable to Statical and 
to Dynamical Problems, which regard Motion as the result 
and the essential fact of Force, whose full expression includes 
as fnctors the Velocity and Mass. 

The Concrete Branches are : — I. The Mechanic Powers, and 
Machinery generally (fluid action not included). Here there 
is an application of the deductive laws, but these have to be 
modified by the molecular structure of bodies ; and the modifi- 
cations are ascertained experimentally. The laws of friction, 
of stress and strain, of molecular transfer in impacts, &c, are 
the subject of experiment almost exclusively. Where deduc- 
tion is applied, it must be submitted at every step to experi- 
mental confirmation. 

II. Hydrostatics and Hydro-Dynamics, or abstract Statics and 
Dynamics applied to Liquids. There is here also the employ- 
ment of experiment to find out the modifications of dynamical 
laws due to the molecular structure of liquids. There is a 
farther use of experiment, in aid of the deductive process 
itself, which is apt to be foiled by the complications of fluid 
mobility. 

III. Aerostatics and Pneumatics comprise the treatment of 
gaseous bodies, to which the foregoing remarks also apply. 

IV. Acoustics treats of vibrations of the air and other bodies, 



CONCRETE DEPARTMENTS OF MOLAR PHYSICS. 

constituting the agency of Sound. Here we have the I 
from the molar to the molecular; but the mode of dealing 
with the phenomenon (through the similitude of pendulous 
and wave motions) has close alliances with the preceding 
molar branches. In this department, however, experiment 
predominates over deduction. 

V. Astronomy might be taken either first or last am 
the Concrete branches. It departs the least from absl 
Statics and Dynamics; which is owing to the purity of tho 
gravitating force ; there being no friction and, in the cele 
region, no resistance. It is deductive throughout ; yet, owing 
to the great mathematical difficulties, the deductions must bo 
checked by continual observation ; while to observation alone 
we owe the knowledge of the co-efficients or constants. 

In Astronomy, there are various problems that draw upon 
the other concrete branches of molar physics, and even upon 
molecular physics ; so that the position of priority amoug the 
concrete branches has to be qualified. The tides, the physical 
constitution of the sun and the planets, the theory of solar and 
planetary heat and light — are examples of these far-branching 
portions of the subject. 

MOLECULAR PHYSICS. 

9. In Molecular Physics, the phenomena have reference 
to the action of the component molecules of matter. 

The chief snbjects are — 

Molecular Attractions — Cohesion, fyc, 

Heat, 

Light, 

Electricity, 
The primary assumption, axiom, or induction of Molecular 
Physics' is to the effect that the masses of matter are composed 
of small particles, atoms, or molecules, attracting or repelling 
each other in various modes, and possessing intestine mot 
This is a real proposition respecting matter, and not a mere 
repetition of its defining property— Inertia. It is pre-emi- 
nently hvpothetical in its character ; that is, the evidenc 
it is only the suitability to express the phenomena open to tho 
senses; as, for example, the solid, liquid, and gaseous forms 
of bodies, the heat or temperature of bodies, luminous and 
electrical effects. 



LOGIC OF PHYSIOS. 



Notions of Molecular Physics. 

Molecule, Atom.— It is known as a fact that every kind of 
matter is made up of very minute portions, called atoms or 
molecules ; the limit of minuteness being hitherto unascer- 
tained. By supposing attractions and repulsions between the 
atoms, we can represent the varieties of solid, liquid, and gas, 
as well as the imponderable forces — heat, &c. The phenomena, 
however, require that there should be different orders of 
atoms or molecules; the ultimate atoms being grouped into 
complex atoms, and those again, perhaps, into still higher com- 
pounds. Thus, the Cohesion atom, the Heat atom, the Chemical 
atoms, the Solution or Diffusion atom, are all hypothetically 
distinct, the assumptions being varied to suit the appearances. 
The definition of the atom or molecule,* therefore, is hypo- 
thetical and fluctuating ; the only constant assumption is a very 
minute element gifted with attractions and repulsions, by which 
is brought about the aggregation into masses. 

Molecular Attractions — Properties of Matter. Nume- 
rous important notions arise out of this department of Physics, 
which discusses the various modes of aggregation of material 
masses, and their causes, real or hypothetical. 

Solid, Liquid, Gas. — These names for the three states of 
matter, have already occurred under Molar Physics, and must 
there have been defined up to a certain point. The exhaustive 
definition of the various forms of solidity falls under Molecular 
Physics. I shall indicate, for ulterior ends, what seems the 
best arrangement or succession of the properties of Solids. 

Crystal. — Antithesis of amorphous. The crystal is not difficult 
to define. The common fact is a regular and constant geo- 
metric form as determined by the angles of the faces or 
boundary planes. A substance, for example, always found in 
cubes, or with right-angled solid angles, is a crystal^ a sub- 
stance that has no regular or constant form is amorphous; 
such is a cinder. Subsidiary to the main idea, are the notions 
— face, axis, nucleus, cleavage, fracture — and the several systems 

* Although the adjective 'molecular* is used in the broad contrast with 
the molar, while the substantive • molecule' also conforms to the usage, a 
more specific meaning has lately been attached to the molecule, in con- 
tradistinction to the ' atom.' An atom is supposed to be chemically indi- 
visible ; a molecule is the smallest combination believed to exist separately. 
There is a hydrogen atom represented by H ; but the hydrogen molecule 
is H H, or H 2 . The molecule of Phosphorus and of Arsenic is each 
composed of four atoms. All this belongs cO the hypothetical part of 
Chemical Combination. 



MOLECUIAK ATTRACTIONS. 

of crystals— Tesseral, Tetragonal, 4c. ; also 
Dimorphism, Allotropy. 

Hard, Elastic, Tenacious, Ductile, Malleable. Tlicso aro 
names for a series of important attributes of solid I 
which there is a corresponding series of contrasting prop 
&-sofi or flexible, inelastic, brittle, inflexible, inductile or « 
e. They are mostly distinct properties, although to 
extent related. They are all strictly definable, and measurable 
in amount or degree by given tests. Hardness is 
to 'change of form, as by scratching or dinting; Elasticity is 
the rebound from compression. Tenacity is opposed to being 
pulled asunder. Ductility is tenacity under the process of 
being drawn out into wire; if the hammer is employed, the 
substance is called Malleable. 

Viscosity is a softness approaching to liquidity. * All bodies 
capable of having their form indefinitely altered, and resisting 
the change with a force proportioned to the alteration, are 
called Viscous Bodies.' (J. Clerk Maxwell). 

Cohesion (Homogeneous attraction). Definable as the mutual 
attraction of particles of the same substance, as iron, flint, or 
ice. The crystalline structure, hardness, and other qualities in 
the previous enumeration, may be expressed as different 
decrees and modes of cohesive energy. Cohesion is therefore 
the hypothetical summary of the properties just named ; and 
its modes are to be accommodated to represent these with 
accuracy. A crystal must have one mode of cohesion, a 
lump of clay, a different mode. The limits of cohesion are 
small ; two" pieces of plate glass will adhere strongly if in 
close contact, but will not attract one another through a 
sensible distance. 

Adhesion (Heterogeneous attraction). A wide-ranging phe- 
nomenon. It is defined — the attraction of particles of one 
substance for particles of a different substance, as when glue 
sticks to wood, mortar to stone, water to wood, &c. Cements, 
Capillary action, Solution, Absorption of Gases, AUojfl — all 
suppose this mode of action. To express the lull details — 
which substances attract which, and with what decrees of 
force— requires a great many propositions! statements, i 
Conveniently given in the mineral or the chemical description 
of each substance. Under the present head, the general 
results should be presented. 

Diffusion, Osmose. — These are properties extending beyond 
what is implied in solution, and even anticipating Chemical 
processes. Still, they are the immediate sequel to the preced- 



4Q6 LOGIC OF PHYSICS. 

in£ group of phenomena. Their definition is a generaliza- 
tion of the phenomena brought to light by the researches of 

Graham. 

Crystalloid, Colloid, Dialysis.— By extending the application 
of Osmose, Graham arrived at a distinction among bodies, 
expressed by the antithesis — Crystalloid and Colloid, whose 
definition is in the highest degree pregnant with important 
attributes. (1) The colloid state is a mode of the anti-crystal- 
line or amorphous modification of matter. (2) The colloids are 
inert chemically, they are not powerful as acids or bases. (3) 
In their own form, they have peculiar powers ; as soft and 
semi-liquid they allow other substances to diffuse in them. 
(i) Still more important is their instability, their readiness to 
pass into change, and gradually to sink down towards the 
deadness and fixity of the crystal ; during which process they | 
are sources of molecular power. These two last peculiarities 
fit them to play a part in living structures, into which they 
enter largely as constituents (albumen, fibrine, starch, &c, are 
colloids). (5) Colloids, while permeable by bodies of the 
crystalloid class, as salt and sugar, are impermeable to each 
other ; a most important law, on which Graham has founded 
his method of Dialysis, and which is the explanation of many 
interesting phenomena. 

Effusion, Diffusion, and Transpiration (of gases). — These are 
the phenomena parallel to the foregoing as manifested in gases ; 
they have a modified definition accordingly. 

Such is an orderly statement of the great leading notions of 
the initial branch of Molecular Physics. They all demand 
strict definition, and a separation of defining properties from 
predicated properties, according to the best logical method. 
Descending into the very depths of molecular action, they un- 
avoidably anticipate other parts of molecular physics, and even 
of Chemistry ; but this is not avoidable by any arrangement. 
The priority of position is justified by the circumstance that 
Cohesive Force is the inalienable attribute of all kinds of 
matter, and is the counter-force to the great total of Energy 
expressed by the Correlated Forces— Heat, &c. Matter is what 
we find it, on the one hand, through the opposing play of 
internal cohesions, and on the other hand through the repulsion 
derived from the transferable energy of the universe. It is 
as Heat, Electricity, and Chemical' Force, that this energy 
ab extra counter-works internal cohesion ; just as, in the 
capacity of mechanical energy, it counter-works Gravitv on 
the great scale of molar movements. 



DEFINITION AND PROPOSITIONS OF HEAT. 

Heat. — The next department in order is the primary and 
the typical form of molecular energy, in the great cin 
served or Persistent Forces. The leading notion— 
itself is the only one attended with logical difficulties 
nition. Properly speaking it is an ultimate, indefii 
communicable notion, and its essential character is iubji 
Each of us must be referred to our own sensations of lie.it and 
cold in their different degrees, which sensations are unique 
and not to be confounded with any others. Nor is there any 
perplexity in generalizing the particulars, with a view- 
comprehensive definition, as there is with matter and inertia; 
he that has one or a few experiences of change of temperature 
knows all. 

The physical or objective counterparts of this unmistakeable 
subjective experience are numerous and various, and belong to 
strictly physical investigation. The most obvious are the 
increase of bulk by warmth, and the so called destruction, 
(more properly re-construction) of material masses. A _ 
and protracted effort of generalization has been requisite to 
encompass all the manifestations of this physical correlate of 
a familiar feeling, and to embrace the whole in a unity of 
expression. Even at the present moment, the generalized 
unity rests upon a hypothetical assumption, true in the main 
fact, but uncertain in the shaping, and as yet imperfectly adap- 
ted to the multiplicity of the thermal phenomena. Heat, 
physically, is a mode of molecular motion, exchanging at a 
definite rate with mechanical movement, as well as with the 
other molecular modes termed Electricity and Chemical force. 
If we define Heat by its subjective phase, the great physical 
generalization is a predicate of concomitance, constituting a 
real proposition. If we use the subjective fact merely as a 
clue to the objective, and insist on making the definition ob- 
jective, this property is then the defining property, from which 
would flow innumerable deductive attributes (propria) ; while 
there would be propositions (either propria or concomit, 
affirming the relationships of heat to other forces, and also the 
materiaf collocations or arrangements connected with the 
transmutation. 

The notions involved in the various phenomena of 1 1 
the heads of the science ; they are all definable I 
tion, and their elucidation needs abundant reference I 
the concrete :— Conduction, Convection, Radiation, 1 
Absorption, Diathermacy, Refraction, Specific Heat* £**0nt 
Heat, Melting, Freezing, Evaporation, Condensation, EbttUl- 



468 L0GI ° 0F physics. 

tion, Boiling Point, Distillation, Tension of Vapour, Dew 
Point, Heat "of Combination, Calorific equivalents. 

Light. — The exact position of this subject in a strictly 
studied arrangement of topics is somewhat dubious. In some 
important points, it has a close alliance to Heat ; its manifesta- 
tion in a body is almost always dependent on a certain 
temperature. Moreover, as an influence radiating through 
space, it has not only great similarity to heat, but also is 
singularly open to mathematical treatment. Still, being as 
yet imperfectly understood in its reciprocation with the cor- 
related forces, it does not stand to heat on the same footing as 
electrical and chemical force. But for the close and easy 
transition from Electricity to Chemistry, we might put Light 
at the end of Molecular Physics. Or, as having abstruse 
chemical relationships, it might succeed to Chemistry. Thus, 
the position actually accorded is owing to a seeming prepon- 
derance in favour of one out of several alternatives. 

Light, like heat, must have a subjective definition to start 
with ; and, in this view, it has the same freedom from ambi- 
guity. But as Sight is a highly objective sense, we can incor- 
porate with the subjective property the objective particulars 
— radiation and transmission in space — which are revealed at 
once to the luminous sensibility. 

We may give the definition thus : — Light expresses a dis- 
tinct state of mind known only to individual self-consciousness, 
to which state is added the objective experience of an emana- j 
tion from a material body to the eye, whereby we become 
cognizant of the characteristic properties of matter named 
visible. 

The subsidiary notions are the main topics of the science : — 
Transparent, opaque, translucent, shadow ; Incidence, Effrac- 
tion, Index of Refraction, Lens, Image, Reflexion, Mirror, 
Caustic, Focus, Colour, Spectrum, Complementary Colours, 
Dispersion, Chromatic Aberration, Diffraction, Rainbow, 
Double Refraction, Polarization, Interference, Undulatory 
Theory. 

So far as these topics are concerned, the science of optics 
depends upon no extraneous source beyond Mathematics, and 
might have precedence of all the other subjects of molecular 
physics. The connexion of Light with Heat, with Electricity, 
and with Chemistry, would then fall under these several 
departments. 

Electricity.— As the denotation of Electricity takes in— 

Magnetism Voltaic Electricity Magneto-Electricity 

h notion Electricity Electro -Magnetism Thermo-Electricity— 



CHARACTERS OF ELECTRIC FOK( 

it is no easy matter to find an exact connotation for tlio 
general name. Two properties may be put forward : (1) 
Polarity, and (2) Current action. As regards the firsfe, 
Polarity, there is uniform agreement in all the modes ; and, 
moreover, the polar attribute is prominent and pervading, 
imparts a destinctive character to all the phenomena. 
in carrying out the idea, we are met by the ambiguous 
nomenon, named by Faraday, Diamagnetism, a force mani- 
fested by the magnet upon heavy glass and certain other 
substances, but without polarity, being equal repulsion by both 
poles. This phenomenon, however, must be held in Buspense 
in the meantime, and not allowed to interfere with the defini- 
tion on so vital a point. 

The second characteristic of the Electric Forces, is their 
being carried to any distance, through solid conductors, so as 
to discharge themselves at any point. In ordinary chemical 
action, as in the double decomposition of two salts, the sub- 
stances mnst be in contact ; but by an electrical arrangement, 
the oxidation of zinc in one vessel, may lead to the decompo- 
sition of water in another. This important point of commu- 
nity makes a strong alliance, although with differences, between 
the electric forces. 

These two leading features, coupled with subjection to the 
great Law of Conservation, are all that can be at present 
brought under the connotation of Electricity as a whole. The 
different branches have each their special definition, attainable 
by the same generalizing process. Definitions are also to bo 
provided for the subsidiary notions — Magnetic Poles, Meri- 
dian, Declination, Inclination ; Electrics, Non-Electrics, Con- 
duction, Insulation, Circuit, Induction, Charge, Discharge, 
Electrical tension ; Electrolysis, Electrodes. 

Propositions of Molecular Physics. 

Axiom of Conservation of Force. — At the threshold of mole- 
cular physics, there must be provided a statement of the Law 
of Conservation, in all its compass, or as embracing alike tho 
molar and the molecular forces. Although the law cannot 
be fully comprehended at this stage, yet some attempt should 
be made to exemplify its workings as Heat, as Electricity, and 
as Chemical force, and also to point out the mutual convei 
of all the modes — molecular and molar. The law is the pre- 
siding axiom of molecular Physics, and of Chemistry, 
through them reaches the domain of Physiology. It is ei 
where the sufficing explanation of the origin of Force 5 leaving 



470 



LOGIC OF PHYSICS. 



to bo investigated, the arrangements, situations, or circum- 
stanced, attending on the manifestation of force in each par- 

ticnlar case. 

(Jlhrr propositions of Molecular Physics. — The various notions 
or defining properties being clearly characterized, we may 
readily ascertain what class of predicates usually go with 
them so as to constitute the real propositions of the science. 
Thus, with reference to the first department — Molecular Attrac- 
tions, or the Properties of Matter, from which are excluded 
whatever comes under Heat, Electricity, and Chemistry — the 
atom or molecule being defined, we have, as real propositions, 
the following : ' Matter is composed of atoms ;' ' the atoms of 
matter attract each other.' This last proposition being one of 
wide generality, there fall under it many special propositions, 
or modes of attraction, for different kinds of matter ; but, in 
this department, we are perpetually disposed to palm off 
verbal propositions for real — as in affirming that hard bodies 
have a powerful atomic cohesion. Examples of strictly real 
propositions are these : — crystals are hard bodies, that is, the 
cohesion of crystallization is intense in degree ; crystals 
are usually brittle, or the cohesion of crystals is of a short 
range. Again, with regard to Adhesion, there is an import- 
ant inductive generalization, that bodies of a nearly similar 
nature are those possessing mutual adhesion ; thus metals 
adhere in solders and in alloys, earthy bodies, in cements and , 
in cohesive mixtures, and so on. Farther, the Diffusive 
volume of a gas is inversely as the square root of its density. 

These are propositions of co-inhering attributes, verified 
only by wide and exhaustive agreement through the whole 
sphere of the things concerned. 

Another large class of propositions under the same depart- 
ment includes the numerical expressions of the degrees of the 
different attributes. These are the constants of the department, 
and need no farther remark. 

The propositions of Heat have the reality arising in the 
concomitance of subject and object facts. Apart from this, 
they may be classified under the following heads. The first 
class takes in the deductions from the law of Conservation, 
confirmed by observation and induction : — such are the facts 
of the dilatation of bodies by heat, of which fusion and eva- 
poration are special manifestations. There is herein comprised 
a wide field of natural phenomena; and many specific state- 
ments are needed to cover the variety of modes in different 
substances. Another class of propositions affirm, in their 



PltOPOSITIONS OF HEAT. 171 

t 6everal modes, the great molecular property named Conduction^ 
a property with numerical degrees; while importan 
dependence or concomitance connect this property with the 
molecular properties of bodies. Radiation next demands to 
be considered, a fact with geometrical aspects and correspond- 
ing predicates ; this part of the subject having a considerable 
parallelism to the leading facts of Optics. The specific i 
of radiation of different bodies may be numerically ascertained, 
and laws enounced, whose character is jointly deductive 
inductive. Absorption is another predicate, and similar 
remarks apply to it. 

The exhaustion of the consequences of the Law of Conserva- 
tion, would require a statement of the mode of deriving heat 
from Mechauical force (crushing, collision, or friction), and 
from the other molecular forces ; and also the situations or 
arrangements whereby it returns to these again ; the case of 
producing mechanical force having been given under the great 
fact of Dilatation. 

On the whole, propositions of heat are (1) Derivatives from 
Conservation ; (2) Constants, or numerical measures of the 
various phenomena for different bodies ; (3) Laws connecting 
manifestations of heat with molecular structure ; (4) Laws of 
situation, or conditions of the transmutation cf Heat, to and 
from, the other energies, with the constants, expressing the 
rates of equivalence. 

The foregoing account may suffice to exemplify the propo- 
sitions of molecular physics. Were w r e to proceed to LlOHT, 
we should find a statement of definite phenomena — called 
radiation, refraction, reflexion, dispersion, colour — all expressed 
under numerical and geometrical relations. We should also 
find some cases of concomitance of attributes, as Double Re- 
fraction and Polarization. The connections of Light with 
Heat and with Chemical Force, being underivab^) from the 
great Law of Conservation, must be given as empirical induc- 
tions of co-inhering attributes, some of them of considerable 
generality, as the connexion of light with temperature; others 
narrow and special, as in the chemical relations. 

Electricity has the advantage of being fully correlated with 
the other forces. It involves, however, great complexity of 
arrangements, as conditions of its manifestation in the var 
species ; whence the propositions are greatly occupied in stating 
these arrangements or collocations ; many of them being hidden 
in the molecular depths of bodies, and rendered in hypothetical 
language. 

21 



|; L ) LOGIC OF CHEMISTRY. 

Predominant Methods of Physics. 

10. Physics has been seen to be partly Deductive, and 
partly Inductive. The Inductions principally relate to 
Cause and Effect ; while, in Molecular Physics, there are 
inductions of Co-inhering Attributes. The principles oi 
Definition are appealed to, and more especially for the 
primary notions ; but there is scarcely any opening for 
Classification. 

As a Deductive Science, Molar Physics is a branch of applied 
Mathematics, checked and controlled by the perpetual reference 
to facts. 

As an Inductive Science, Physics makes an unsurpassed 
display of the machinery and resources of Observation and j 
Experiment. It also shows to advantage all the Methods of 
Experimental Elimination. The facts being subject to the 
great law of Conservation, the deeper experimental problems j 
consist in ascertaining the collocations or arrangements for"! 
transmuting or evolving the different modes of force. The 
researches and discoveries relating to Heat, Electricity, and 
Light have this character to a very large degree. 

The Hypotheses of Physics exemplify all the forms of Hypo- \ 
thesis formerly laid down. The chief instances — the Dynamical 
Theory of Heat, the Undulatory Theory of Light— have already 
been adduced in expounding the general subject. Another 
hypothesis of inferior weight and character is the two Elec- 
trical Fluids, for representing the polar phenomena of Eleo- < 
iricity. 



CHAPTER III. 

LOGIC OF CHEMISTEY. 

1. The relationships of Chemistry to all the departments 
of Molecular Physics are intimate and sustained. The 
special fact of the science is given in the name Chemical 
Attraction. 

Chemistry deals with the union and the separation of ele- 
ments ; it regards all the substances of nature as either simples 



REAL PREDICATIONS OF CHEMISTRY. 

>r compounds; the manner of union or composition I 
ipeciai to the science. There are unions not chemical 
,vhen bodies are pulverized and mixed together wit bout farthi r 

ntimacy. There is a still more intimate union m 
■vhich, however, also comes short of chemical union. 

2. Chemical Attraction, or Union, involves these i 

1) The Properties are definite. (2) In the act of union, 
fibere is Heat evolved. (3) The chief properties oi the 
dements disappear. 

A fourth mark, which may either enter into the definition, 
>r be reserved as a predicate, is that chemical union takes 
}lace between dissimilar substances, while solution or adln 
s between similars. If reserved as a predicate, this property 
jrfll be one of the properties forming real propositions, us ex- 
emplified in next section. 

It is not necessary here to exemplify these defining proper- 
:ies. In a work on chemistry, it would be advisable to offer 
n advance a few illustrative cases, as a preparation for enter- 
ng on the systematic detail. 

This disposes of the leading notion of Chemistry, being the 
essence or connotation of the name, the Definition oi* the 
Science. A mistake in Logic is made when these properties 
ire stated as real propositions ; they are not predicated of a 
mbject called Chemical Attraction, they constitute or make up 
ihat subject. 

3. The Propositions, or real predications, of Chemistry 
relate (1) to the circumstances, or conditions of Chemical 
jhange, (2) to the substances that undergo the change. 

(1) When we have defined the fact of Chemical union, 
(with its correlative and implicated facts, Decomposition, 
Simple Body, Compound Body), we have to state the various 
3ircumstances, conditions, or modifying influences of Chemical 
mange. This constitutes numerous real predications, of great 
:heoretical and practical moment. 

(2) The enumeration of substances that combine together 
3hemically, or that bring about chemical decompositions yields 
i large mass of real propositions, under the general predicate 
pf Co-existence, or Co-inhering attributes. Oxygen c 
aines with hydrogen, and forms water; sulphuric acid decom- 
poses chalk, common salt, &c. 

The expressions for the definite combining numbers are real 
propositions, corresponding to the 'constants 1 of Phy 



4*4 LOGIC OF CHEMISTBY. 

The relation of Chemical Force to the other Correlated 
Forces may be re-iterated at the commencement of the subject ; 
although, as with the other preliminary statements, the under- 
standing of it will grow with the unfolding of the future details. 
Arrangement and Methods of Chemistry. 

4. The division of Chemistry is into Inorganic and 
Organic. 

Inorganic Chemistry is laid out under the succession of 
the Simple Bodies. 

The distinction of Inorganic and Organic would exemplify 
definition with a broad doubtful margin. The basis of the 
distinction is the circumstance that a large class of highly 
important substances can be obtained only from living bodies; 
such are starch, sugar, albumen. This peculiarity of origin is 
associated with two other peculiarities, namely, the limited 
number of elements in organic bodies, and the great complexity, 
of the chemical constitution. There would be a convenience in 
adopting all the three facts as a complex definition of Organic 
bodies, from which, by antithesis o,r negation, we have the 
definition of the Inorganic. 

The Chemistry of the Inorganic or Mineral world comes 
first ; and its method of arrangement is to adopt some succes- 
sion of the Simple Bodies, and under them, to distribute the 
various Compounds, 

Classification of the Simple Bodies or Elements. 

5. The Simple Bodies, or Elements, are divided, in the' 
first instance, into Metals and Non-Metals. Although 
there are transition elements, as Tellurium and Arsenic, 
the distinction is founded on important differences. 

The Metals have certain prevailing characteristics, but yet 
in a varying degree, and with occasional exceptions. (1) Most 
striking are the visible properties— Opacity, Lustre, and Colour. 
Metals are opaque; they have the peculiar lustre termed metallic; 
and their colour is white or grey, with the exceptions— Gold, 
Copper, and Titanium ? which are yellow. (2) They are solid, 
Mercury .and Hydrogen being notable exceptions. The solidity 
is usually joined with compactness of structure, as shown in 
the properties— hardness and tenacity. (3) They are com- 
paratively good conductors of Heat. (4) They are conductors 
ot Electricity. (5) They are Wectro-positive. (6) They com- 



METALS AND NON-METALS CLASSIFIED. 

bine chemically with the Non-Metals. (7) Their componndi 
with Oxygen are for the most part Bases, and nol 

The question is not here raised how far so pro- 

perties are implicated in others. Since the implication 1* Dot 

obvious, the properties are provisionally given a 
more important remark, from the logical point ol view, ia the 
jccurrence of exceptions to almost all the properties. Jn the 
complex defining of natural objects, we must he prepare 
this circumstance, which does not render the classification 
or nugatory. Although mercury is a liquid we neither 
render the property of solidity, nor exclude it from tin- - 
Solidity is wanting only in two; and mercury has all t ho 
other six properties. This is probably one of the cases where 
Whewell would desiderate a type, or average representative 
specimen, some metal possessing in fair measure all the 
prevailing characters. 

The Non- Metals are defined by the antithesis cf the ab 
group of properties. As regards Light they are not uniformly 
opaque, and when opaque, they are, except selenium, wan 
in lustre. There is only one Gaseous metal, there are four 
gaseous non-metals. They are non-conductors of Electricity, 
and Electro-negative. Their compounds with oxygen (one of 
their number) tend to Acids, and not to Bases. 

Whenever a classification is possible, there must be common 
properties, and these are possible to be stated. Still, in the 
usage of Chemical writers, the statement of the generic pro- 
perties of the classes 'metal' and 'non-metal,' does no* 
pense with the repetition of these in the detail of tlu 
The Natural History methods, not being susceptible of exten- 
sive application in Chemistry, are hardly attended to, even 
where admissible. Nevertheless, as the situations arising in 
the classification of the Simple Bodies are highly illustrative 
of situations in Botany and in Zoology, we may follow out 
the present case a little farther. 

6. Both Metals and Non-Metals are sub-divisible into 
smaller classes or groups. 

In the Metals, there are certain groups that have important 
affinities — such are the Alkali-Metals (Sodiu 
Alkaline- Earth Metals (Barium, &c), the Earth-M< 
(Aluminium, &c), the Noble Metals (Mercury, Silv< 
&c.) remarkable for refusing combination. A group is also 
cated by the important fact — exceptional to the tendency of the 
metals as a whole — namely, forming acids with oxygen. A 



47G LOGIC OF CHEMISTRY. 

presenting analogies to iron, make an Iron group— Manganese. 
Cobalt, Nickel, Chromium, Uranium. A certain amount ol 
mblance suggests the juxta-position of Zinc, Cadmium and 
Magnesium. (Miller's Chemistry, x L 11). 

The expository succession adopts the order of greatest 
resemblances. The succession is necessarily linear, and leads 
inevitably to the wide removal of bodies that agree in some 
important particulars. The idea is sometimes conceived of a 
circular, or superficial arrangement for bringing together 
resembling bodies on two sides ; while, by a diagram of solid 
dimensions, each body may be brought into relationship on 
three sides. Still, the expository order can follow but one 
course, indicated by the maximum of resemblance ; and pro- 
vision has to be made under each body for indicating agree- 
ments between it and bodies in other groups. 

There can scarcely be any doubt as to the propriety oi 
placing the substances of strongest chemical affinity at one 
end of the line (Hydrogen, Potassium, &c), and of weakest 
affinity at the other end (the noble metals). 

The Non-Metals (13 in. number) contain a few groups, and 
some isolated individuals. The halogen group of Berzelius — 
Chlorine, Bromine, Iodine, and Fluorine; and the sulphur group 
— Sulphur, Phosphorus, Selenium, and Tellurium — are classed 
as having considerable and important resemblances. SiHcoa 
and Boron have points in common : and their suffix on was 
given to show some small analogy between them and carbon,! 
The substance of most marked isolation is Nitrogen ; while 
Oxygen is pre-eminent by the catholicity of its chemical 
affinities. 

By unanimous consent, Oxygen has precedence. The second 
place is variously assigned. To take up Hydrogen could 
never have been strongly justified, and is now less so than ever.' 
For the single advantage of having Water brought forward at 
an early stage, a leap is taken to the extreme opposition, 
making the last first. Most is to be said in favour of Nitro- 
gen, as the second body. Remarkable for its chemical neu- 
trality, it also gives an opportunity for dwelling on the 
mechanical peculiarities of gaseous elements ; and it may be 
followed up by the consideration of the Atmosphere— a me- 
chanical admixture of Oxygen and Nitrogen. 

Except to hurry on to familiar and interesting combinations 
there is no need to bring forward carbon among the very 
first ; the nearest kindred to oxygen is found in the halogens 
—Chlorine, &c. To these might follow Carbon, and perhaps 



PLACE OF EXPOSITION OF COMPOUNDS, 

Boron and Silicon, while the Sulphur group would 
irray. Leaving the question open, whether Carbon, i 
ind Boron, should one or all precede or follow the Sulphur 
Troup, the rule of arranging by the maximum of agra 
m the whole would be best carried out thus : — 

Oxygen, Chlorine, Carbon, Sulphur, 

Nitrogen, Bromine, Boron, Phosphurma, 

Iodine, Silicon, 

Fluorine, Tellurium. 

Since the exposition of Chemistry follows a certain order of 
the Simple Bodies— the Non-Metals first, and the Metals next— 
some consideration is necessary iu order to assign a place for 
the Compounds, which far outnumber the Elements. As it 
would be inconsistent with the very nature of the subject to 
separate the Compounds frcm the Simples, seeing that the 
chemical characters of a simple body are expressed by its 
forming compounds with other bodies, the Compounds must 
be interpolated in the exposition, and appended to such of the 
Simple Bodies as they are most intimately allied with. 

Hence there will always be a choice of positions ; the com- 
pound 'water' may be attached either to the element oxygen, 
or to the element hydrogen. 

There is one obvious consideration applicable to this peculiar 
emergency. A compound need not be brought forward for 
full description till all its elements have been stated ; water 
may wait till hydrogen is given ; carbonic acid may follow 
carbon, oxygen being previously given ; the salts may be 
appended to the metals that are their bases. Yet this arrange- 
ment is not without its disadvantage. The element given 
last may not be considered the most important in regard to 
the characters ; thus hydrogen is the completing element of 
so many important compounds, as, for example, the hydr 
acids, that, supposing it placed at the head of the metals, it 
would be followed by an enormous crowd of compound sub- 
stances ; many of which would seem more naturally related to 
other elements, as the acids to their several radicles — nitr< 
chlorine, sulphur, &c. 

The difficulty in this particular instance may be §upp 
to be got over, by the expedient of bringing on hydrogen 
after oxygen. The operation, however, begins by an & 
violent transposition that may be expected to land us in I 
other fix. And so it is. Enabling us without loss of principle 
to attach the acids to their several radicles — nitric acid to 
nitrogen, &c, the proposed step compels an abrupt stoppage 






LOGIC OF CHEMISTRY. 



where there is a natural transition, namely from the acids to 
the salts. In point of fact, the barrier is always forced at this 
point- the salts are brought in, notwithstanding that the 
metallic bases are still far ahead. Thus, after all, the trans- 
planting of hydrogen from its proper allies merely postpones 
an inconsistency for one moment. 

On the other hand, it may be maintained that the proper 
place of the important hydrogen compounds is after hydrogen ; 
its most characteristic feature being to constitute and com- 
plete these compounds. The class 'hydrogen acid' is connoted 
by the presence of hydrogen; sulphuretted hydrogen and 
sulphuric acid are more in place among hydrogen acids than 
among sulphur compounds. This alone would be a strong 
reason for not bringing on hydrogen till the end of the non- 
metals, in which are contained the other acid constituents. 
If these acids are disposed of first, the interest of hydrogen is 
used up ; except as composing water, everything about it is 
become stale. 

Descriptive Characters of Chemical Substances. 

7. The description of bodies in Chemistry, whether the 
Simple Bodies or Compounds, should coincide with the 
expository order of the properties — physical and chemical. 

In Chemistry, no less than in the Natural History sciences, 
a regular and uniform plan, in the descriptive arrangement, is 
more than an aid to memory ; it is farther an instrument of 
investigation. The plan adopted in Chemistry, slightly modi- 
fied, will serve also in Mineralogy. 

The Cheniist professedly exhausts the physical as well as 
the chemical characters of each substance. Hence the scheme 
should comprise both groups in the best order of succession ; 
which order, as regards physical properties, is seen in the 
exposition of Molecular Physics. There are some open points 
of arrangement, chiefly with reference to the Crystalline form 
and the Optical properties. Apart from these, the succession 
woold be Molecular Cohesion, Heat, Electricity. If the 
Crystalline form is viewed in the first instance as a purely 
geometrical fact, it might take precedence of all Physical 
properties. The Optical properties, stated as such, without 
enquiring into their connexions with molecular structure or 
with ; chemical arrangements, might be given next. The 
priority of these two properties would have the expository 
advantage of mentioning first what soonest strikes the senses ; 



OEDEIl OF DESCRIPTIVE CHAKACI. j;,, 

the eye taking the lead in the scrutiny of whatev* 
trie. 

To the Crystalline and Optical properties might succeed the 
Specific Gravity. 

Next in order would be the properties hypothetically re- 
joined as modes of Coiifsion :-— Hardness, Tenacity, I 

There would then succeed the properties summed up in 
^Dl[^:sION:— Solution, Diffusion, Osmose, Elfusion and Trail* 
| piration (of gases). 

The relations to Heat, are given in the following proper- 
ties: — Rate of Dilatation; Melting and Boiling Tempera- 
tures; Conduction; Specific Heat, Latent Heat, Radiation, 
Absorption, Refraction, Polarization. 

Relations to Electricity : — Magnetic Property ; Conduct ion 
3r Insulation of Friction Electricity; Conduction or Insulation 
:>f Voltaic Electricity ; place in the Electro-positive to Electro- 
negative series ; place in the Thermo-electric series. 

The Chemical properties are — Chemical Composition (if not 
m Element); the bodies that the substance combine with ; 
the circumstances of the combinations ; and the agency of 
3ach in decompositions. 

Of these characters, two — Adhesion and Chemical Attrac- 
tion — are by their nature correlative characters ; they involve 
the mutual action of at least two substances. With reference 
to them, the property of any one body is relative to soino 
second body ; a substance is not universally adhesive, nor 
universally disposed to chemical unions. Hence the account 
Df the Adhesive and the Chemical properties is complicated 
incl not easy to manage. There is from this cause, an especial 
difficulty in giving an adequate notion of the 1 ionics that 
happen to come first; indeed it is impossible to do jtrstic 
Oxygen, for example, until a great many more bodies are 
described, namely, the long list that oxygen combines with. 
The proper course, in such circumstances, is to avow the 
difficulty, and not to expect that a learner can receive orlier 
than an inadequate or half notion of Oxygen, until he has 
xmie on to the full description of such bodies, as Carbon, Sul- 
phur, Hydrogen, and a few of the metals. 

Examples of Deccription. 

(1) Light. — A gas. Transparent and colourless. Index of 
Refraction 1.00027. 

(2) Specific Gravity 1.1056 ; the atmosphere being 1. 

(3) Adhesion far ether substances. — Solubility in water, :. 



4S0 LOGIC OF CHEMISTRY. 

about one twentieth to one thirtieth of its bulk (.04114j a1 
P. ; .02989 at 59° F.). 

(4) Relations to Heat. — Rate of Dilatation not stated. As 
rds the temperatures of Liquefaction and Freezing, has 

never been liquified, although condensed to -5-JUj of its bulk. 
Specific Heat, about one fourth of water (.2405). 

(5) Relations to Electricity. — Is a magnet at common tem- 
peratures. In the Voltaic series, it is at the head of electro- 
negative elements. 

(Ij) Chemical relations. — Speaking generally, it is the most 
widely-combining element in nature. With a doubtful excep- 
tion (fluorine), it combines with every known element; not 
merely its natural opposites, the metals, but non-metals like- 
wise. Classes of leading importance in chemistry are com- 
pounds of oxygen with the other elements ; the oxides of the 
metals are what are termed bases ; the oxides of the non- 
metallic elements are generally acids. With Hydrogen, it 
yields ivater* The act of combining with Carbon, either alone, 
or along with hydrogen, is the most familiar example of 
violent and rapid chemical union, with evolution of heat and 
of light, and is termed ' combustion/ 

The peculiar circumstances attending the combinations of 
oxygen vary with the character of the second element. Thus, 
in the leading fact — Heat of combination — the maximum 
evolved is with Hydrogen; Carbon yields one fourth of that 
amount ; Phosphorus, about a sixth ; Sulphur, about a 
fifteenth ; Zinc, Iron, Tin, about a twenty-sixth. 

Atomic number, 16. 

As regards the conditions of entering into combination, '. 
there is great variety, from the extreme of readiness at the 
ordinary temperature of the atmosphere, to the extreme of 
indifference, conquered only by the aids to combination, 
namely, artificial condensation, heat, the electric spark, the 
continuity of chemical action already begun, &c. Part of the 
peculiarity is due to the state of oxygen itself: — which may 
be either in the ordinary atmospheric dilution ; or prepared 
apart free from any other gas (whereby all combinations are 
acclerated) ; or, lastly, in combination with other bodies as 
in water (a powerful oxidizer) ; in the nitrates, in chlorate of 
potash—which salts permit of the liberation of their contained 
oxygen in a highly concentrated form. 

Local spread of Oxygen,.— Need not be here detailed. 

Modes of obtaining Oxygen. 

I doubt the propriety of including, under Oxygen, any more 



1 



OXYGEN DESCMBED. 



detailed account of the oxygon compounds. Thcro n 
opportunities afterwards, under the several elemi 
the other members of the compounds,— carbon, bydn 
metals, &c. Nor is it necessary to bring forward Co 
of which a sensational use is commonly made, in the 
tion of oxygen. A disproportionate prominence is th 
given to what is, strictly speaking, incidental only f 
the modes of oxidation, and is found in other chemical 
binations if they happen to be rapid and energetic. Combo 
is a special thesis under the general head— Chemical Union, its 
conditions, and circumstances — and is of great importance 
both theoretically and practically, but it need not be appei 
to Oxygen. If involving too much anticipation of detail 
be given in the preparatory view of Chemical Combination 
(where, however, it might be briefly indicated), it might be 
Drought in at some convenient point, by way of digrett 
as for example, at the end of Carbon, the chief element in 
ordinary combustion. 

Ozone. — A supposed allotropic form of Oxygen, under 
which the oxygen is rendered more active in entering into its 
various combinations. 

The specific gravity of ozone is greater than of oxygen. 
Adhesion. — It is not soluble in water, nor in acids or in 
alkalies ; but it is soluble in iodide of potassium. 

Relations to Heat. — Its active character is destroyed by a 
temperature not much above boiling water. 

Relations to Electricity. — The transmission of a series of 
electric sparks through dry oxygen is one of the modes of 
producing it. 

Odour. — It has a characteristic odour, whence its name.* 
Chemical properties. — While it does not combine with any 
6ubstance but those that oxygen combines with, it combines 
at temperatures, and under circumstances where oxygen docs 
not combine. Hence it is a powerful oxidizing agent — in oxi- 
dizing metals, in destroying vegetable and animal compounds, 
in bleaching, in purifying the air from miasmata, in stimulating 
the respiratory organs. 
Modes of preparing Ozone. 

Remarks on Ozone.f — It is interesting to note the power of 
electricity to give a new combining aptitude to oxygen. 

* Taste and Odour may provisionally be given after Electricity, And 

bffore Chemical properties. They are doubtless a consequence of C: 
calie. actions. 

-t The heading ' Pwemarks' is intended, among other uses, to avoid tho 



482 



LOGIC OF CHEMISTRY. 



Nitrogen.— A gas. 

As regards £^, transparent, colourless; detracting In- 
dex, 1.0093. 

Specific gravity.— .9713. Atmosphere J. 

Adhesion.— Water dissolves about a thirtieth of its bulk at 
ordinary temperatures. 

Relations to Heat. — Dilatation not stated. Never been 
liquefied. Specific Heat, slightly less than Oxygen, .2368. 

Relations to Electricity.— Next to oxygen in the Electro- 
negative series. 

Chemical relations.— Nitrogen enters into a very limited 
number of compounds. Where it does combine, it is sin- 
gularly inert, or indisposed to enter into combination ; de- 
manding to be placed in the most stimulating conditions. 
Many interesting consequences in vegetable and in animal life 
are traceable to this peculiarity. 

Compounds with Oxygen. — Recited in so far as illustrating 
Nitrogen. 

Compounds with Hydrogen. — Ammonia, &c. 

Compounds with Carbon. — Cyanides. 

Spread of Nitrogen. — Modes of obtaining it. Remarks : — 
bearings upon Chemical theory. 

The next example is a solid element. 

Carbon. — A solid, in two states — crystallized Diamond, and 
amorphous Graphite. These occur in such a degree of purity 
that they may be taken as typical of the element. 

(Diamond). — The Crystallization, Optical Properties, Speci- 
fic Gravity, need not be here recited. 

Cohesion. — The hardest body known ; hence at the top of 
the scale of mineral hardness. 

Adhesion. — A very important circumstance as regards other 
forms of carbon, but not ascertainable in the diamond itself. 

Relations to Heat. — Is not fused or volatilized by the highest 
known heat ; is not known to exist either as liquid or as vapour. 
An intense heat merely reduces it to a black opaque mass. 

Relations to Electricity. — A non-conductor. Carbon has a 
high relative place in the Electro-negative series (place given). 

Before stating the chemical relations, a similar recital should 
be given for the other form, Graphite. 

Chemical relations. The range of elements combining with 
carbon comprises — Oxygen, Nitrogen, Hydrogen, Phosphorus, 
Sulphur, and many Metals, especially Iron. It does not enter 

confusion and perplexity of introducing speculative considerations into 
the methodical description. 



DESCRIPTIVE MITIIOn. 

into combination nnless at high fcemperatm 
bines with rapidity and copious evolution of h< 

Compounds with Oxygen.— Carbonic Acid, Carb >nio I 

(described at full length). 

With Nitrogen.— Cyanogen ; alluded to. 

The other compounds may be postpone I. 

Spread and Sources of Carbon. — Imp q& 

marks on Carbon. — Combustion. 

These examples are sufficient for the purpose of in 
a systematic mode of describing the element 
would apply equally to compounds. In them, however, the 
chemical relations involve another circumstance, namely, the 
modes of decomposition. 

In certain of the elements, the chief practical inter. 
found in impure forms — alleys, or mixtures with other in- 
gredients; for example, Iron. Still, it is desirable, for I 
retical completeness and consistency, to advert, in the 
instance, to a pure or typical form, in order to know what the 
substance is in itself, both physically and chemically, 
alloys or mixtures may then be given ; but before their 
practical bearings are touched upon, their properties are 
to be recited as illustrating the changes brought about by 
mixture, thereby contributing facts to the inductive laws 
of Adhesion. 

8. In Descriptive Method, it is of importance not to 
mix explanations and theorizings with the description. 

In describing a quality, the first thing is to state precisely 
what it consists in, or how it is discriminated. Moreovei . 
whole series of qualities should be gone through, in the first 
instance, and no attempt made to connect them with 
another, or with other properties, in general laws. 
last operation should always be kept distinct. The 
applies to every science where description enters. 

9. When bodies are closely allied in their natti 
are in consequence grouped as genera, the:: 
should be exhibited in marked contrast. 

The Halogens among the non-metals, the JM tho 

Alkalies, &c, make groups or genera, with agree 
ties. These points of agreement ai 
as to abbreviate the details of the b 
next be given to contrasting pointedly the B 
anions themselves. Thus Sodium and Potassin to a 



4 g^ LOGIC OF CHEMISTKY. 

v.ry large extent; and after the agreements, tlie differences 
should be given in a tabular antithesis. 

10. The generalities of Chemistry are Empirical Laws, 

The Atomic Theory is commonly said to be the highest 
generalization of Chemistry. This, however, must be 
guardedly stated so as not to confound definition with pro- 
positions. The nature of Chemical Attraction is expressed in 
a complex definition (Definite numbers, Production of Heat, 
Merging of elements). There may be real predication in 
declaring these three facts to be conjoined ; and their con- 
junction may be resolved into higher laws, or converted from 
an empirical to a derivative conjunction. 

The propositions, in connexion with Chemical action, that 
have in the highest degree the character of real concomitance, 
are those that affirm the conditions, arrangements, or situa- 
tions attendant on combination and on decomposition. 

For example, Combination requires proximity of the ele- 
ments, and is favoured by all the circumstances that aid 
proximity, as liquefaction ; it is resisted by strong cohesive or 
adhesive forces, and proceeds as these are released. It is 
brought on by elevation of temperature in numerous instances. 
It is induced by the electric spark ; which may operate by 
mere rise of temperature, but more probably by polarizing the 
atoms. It is promoted by concurring combinations ; it accom- 
panies decompositions. These are all empirical laws. They 
are, moreover, statements as to general tendency, and need to 
be accompanied, each with a schedule, stating the individual 
substances and situations of their applicability. 

Many other laws might be cited : — The celebrated law of 
Berthollet, regarding the double decomposition of salts ; the 
laws that simple substances exhibit the strongest affinities, — 
that compounds are more fusible than their elements, — that 
combination tends to a lower state of matter — from gas down 
to solid. 

As Empirical laws, these have no other verification but 
Agreement ; they are only surmised to be laws of causation ; 
they are limited to adjacent cases. 

11. The ultimate generalizations of Chemistry must fall 
under the Law of Conservation of Force, and must express 
the most generalized conditions of the re-distribution of 
Chemical Force. 

The Law of Persistence over-rides every phenomenon of 



HYPOTHESES IN CHEMISTRY. 

change, but it must be accompanied in i 9 with laws of 

Collocation. In Chemistry, there must be indicated the 
cise conditions of chemical re- distribution, whether in 
bmation or in decomposition. It is necessary to fin 
the most general form, the situation or situations ; 
about chemical change, in either direction. It' this can be 
comprehended in one law, that will be the ulti- 

mate law of Chemistry, the Chemical appendage of the Law oi 
Conservation. The Empirical laws above quoted will 
have the improved character attaching to Derivati . 

12. Chemistry contains, as a part of its nature, nui 
reus Hypotheses. These are mainly of the clas s 
Representative Fictions. 

To express in the most general terms the numerous ph 
mena of combination and decomposition, certain arranger 
of the component elements of the compounds are assumed 
hypothetically. It is a, fact that sulphate of potash contains 
certain proportions, by weight, of sulphur, oxygen, and j 
sium ; it is a hypothesis that the salt is made up in the 
particular way shown by the formula KO,S0 3 , being a binary 
compound of two other compounds. 

The Atomic Theory of Dalton contained a generalization of 
facts embedded in Hypothesis. The facts were the fixed pro- 
portions of bodies combining chemically; the hypothesis, that 
each substance is composed of atoms, and that, in chemical 
union, an atom of one substance joins with one, or with two, 
or w T ith more atoms of another ; there being always a neat 
numerical relation without remainder. No one now regards 
this as more than a representative fiction, unsusceptible of 
any other proof than its facility in expressing the fa< 

The Constitution of Salts is the great battle ground of 
chemical hypotheses, being the key to the entire struct air of 
chemical representation. There is, however, a perfect under- 
standing as to the nature of the proof to be offered for the 
rival hypotheses, namely, the suitability to comprehend the 
greatest number of chemical re-actions, or combinations 
decompositions. It is a question purely chemical, and D 
anvwise logical in the sense of demanding attention to i 
called to neglected logical principles. 

As examples of the subordinate hypothetical points, we may 
quote the singular idea of supposing an element to combine 
with itself — hydrogen with hydrogen, chlorine with obi 
and so on ; a very great stretch, seeing that opposition o; 



4SG LOGIC OF CHEMISTRY. 

rncnts is a predicate of chemical union. A better example of 
a likely hypothesis is the proposal to assign to bodies of dif- 
ferent properties, having the same ultimate constitution, a dif- 
ferent proximate constitution; as formic ether and acetate of 
inethv]. The bold hypothesis of Gerhardt and Griffin — to re- 
gard as two substances, iron when entering into proto salts, 
and when entering into sesqui-salts, and the same with all other 
elements producing sesquioxides — was considered as a relief 
from otherwise inextricable difficulties. 

The hypothesis of the Atom, or lowest chemical constituent 
is now coupled with another hypothetical entity — the molecule 
representing the smallest number of atoms of each substance 
supposed to possess separate action. Thus the molecule 
of nitrogen is said to be made up of 2 atoms ; the phosphorus 
and arsenicum molecules, 4 atoms, and so on. 

"When a number of different salts are in the same solution, 
as in a mineral water, it is a matter of hypothesis which acid 
is attached to which base. (IMiiler's Chemistry, II. 624.) 

The class of Scientific Hypothesis consisting of unverified 
theories, does not require special mention in Chemistry. Apart 
from the representative fictions, essential and permanent in the 
science, there are no hypothetic forces or agents. The great 
prevailing agent or cause of chemical change is, and can only 
be, a molecular aspect of the great primeval force named under 
the Law of Conservation. Until the supplement of this law, 
as regards chemical transformation — the universal conditions 
or collocations — be worked out, there will be many hypotheti- 
cal collocations, which will be susceptible of final proof or 
disproof. 

Nomenclature and Classification of Chemistry. 

13. The Nomenclature and the Classification of Chemi- 
stry involve these points :— (1) The use of a symbol for 
each elementary substance ; (2) The expression of the 
ultimate constitution of compounds ; (3) an expression of 
the supposed proximate constitution of each compound in 
a manner suited to its re-actions with other bodies. • 

(1) The symbolical notation has the advantage of affording 
a brief and yet full expression to the most complicated com- 
pounds, rivalling, in this respect, the notation of Mathematics. 
It also enables bodies of like composition to be readily classed, 
and their class indicated to the eye. 

The nomenclature for expressing in terms the various bodie3 



CHEMICAL 

is made up of the names of the elen 

Iron, Silver — and of a systematic mode of a 

compounds — carbonic acid, carburet 

compounds are stateable in this way ; a b 

expressed in some supposed binarj 

rate of potash, chloride of forrayl. *S i 
rch, albumen, are crimen in their familiar 
able naming is, in Chemistry, a sp vial and limil 

and has no analogy to the nanus of species in I 

ZooJ 

(2) The notation exhibits the ultimate CO a of all 
compound bodies, by stating their constituents an I I 
portions of each ; IL is the analysis of water ; FeO, le 
of iron ; Fo 3 , peroxide or sesquioxide. P 

(3) The symbols are farther accommodated to give the 
hypothetical upbuilding of the elements in compli 

pounds ; as in the theory of Salts. The ultimate analysi 
the amount of oxygen in a compound, and the formula 
in what ways the oxygen is supposed to be distributed ; an 
oxygen salt, in the old theory was a binary compound 
two oxidized radicles, the oxide of a non-metal (as sulphur) 
and of a metal (as iron) ; sulphate of iron (protozide ' ). 

The analytical (or Empirical) formula of acetic acid is C 4 II, 4 ; 
of the rational or hypothetical formula, there are no less tfa i 
seven renderings (Miller's Chemistry, vol. Ill , p. G). 

1-i. A desideratum in Chemical Nomenclature 

statement of the structural Heat of the bud: 

The formula H 2 is given indifferently for steam, 
and ice ; although the exact difference of structural beat in 
the three admits of numerical statement. Calling ice N : O ; 
we may call water H 2 + 180° ; steam II, + 11 
the usual reckoning of the heat of boiling and of e >n. 

» Farther, when Hydrogen and Oxygen combine, there La 
a great evolution of structural heat, which is lost to th< 
pound; a provision might be made for indicating the 
figure, which has been found out by experiment ; 
minute quantity would be attached to 1L 0, on this account* 
and about one fourth of that quantity tu C 0* 



CHAPTER IV. 
LOGIC OF BIOLOGY. 

1. Biology is the Science of Living Bodies — Plants and 
Animals ; its exact definition is the definition of Life. 

Definition of Life. 

2. Life is to be defined by a generalization of what is 
common to Living Bodies. 

The Denotation of the term Living Body is well fixed; 
there is scarcely even a debateable margin between the 
Organic and the Inorganic worlds. 

Choosing Assimilation as a characteristic fact of bodily life, 
and Reasoning, as an example of mental life, and contrasting 
both with the characters of dead matter, Mr. Herbert Spencer 
arrives at the following highly complex definition : — 

1. Life contains a process or processes of change. 

2. The change is not a simple or individual act, bnt a series 
or succession of changes. 

3. Life involves a plurality of simultaneous, as well as suc- 
cessive changes. 

4. The changes are heterogeneous, or various in character. 

5. The various changes all combine to a definite result. 

6. Finally, the changes are in correspondence with external 
co-existences and sequences. 

^ In sum : — Life is a set of changes, simultaneous and succes- 
sive, combined to a definite result, and in correspondence with 
external circumstances. Or, in a briefer form, Life is the 
continuous adjustment of internal relations to external rela- 
tions. 

So carefully has the comparison been conducted, that no 
exception could be taken to any part of this definition. Every 
one of the particulars occurs in all living bodies, and in no 
kind of dead matter. The apparent defect of the definition is 
omission ; it does not express or seem to suggest points that 
strike the ordinary observer. For example, there is no allusion 
to the organized structure, at the foundation of which is the 
peculiar constituent known as the cell, or nucleated corpuscle. 
Again, there is no mention of the individual and independent 



ELEMENTS OF LIVING BODIEI £gg 

existence of living bodies; with which is also e i tho 

cycle of birth, growth, and death. 

These omissions, real or apparent, might be defended or 
explained on one of three different grounds. 

First, it might be said, that the facts mentioned, alth< 
present and conspicuous in many or in most living bodie 
not found in all, and therefore cannot be adopted into tho 
general definition. They can bo taken notice of only in 
defining the classes or subdivisions of the whole kingdom of 
animated nature. This remark would be a sufficient justifica- 
tion, if it were true ; but it is not true, at least to the extent 
of excluding the mention of the circumstances from the 
definition. 

Secondly, it might be said, that the definition does not aim 
at being exhaustive, but only at being discriminative ; while 
it is based on essential characters, it does not profess to give 
all the essential characters. Enough is given to prevent us 
from ever confounding a plant or an animal with a stone ; 
but there is no intention of stating every feature that separates 
living bodies from the inanimate world. 

To this the obvious reply would be, why should nil tho 
essential characters not be given ? There is no apparent 
reason for omitting in the statement whatever can be dis- 
covered as common to the whole department of animated 
nature. 

Thirdly, it might be alleged, that the aspects in question 
although not appearing on the surface of the definition, are 
yet implicated on it, and are unfolded in the due course of the 
exposition. The definition, it may be said, goes to the root of 
the matter ; while all else branches out from that, and is duly 
unfolded in the subsequent exposition of the science. 

In order, however, to bring forward at once whatever can be 
assigned as general characters of living bodies, whether 
primary or derived, we shall re-cast the definition, and dis- 
tribute it under the heads — Constituent Elements, Structure, 
and Functions. 

3. I. Living bodies are constituted from elements com- 
mon to them with the inorganic world. 

The chief constituents of Living bodies are these four — 
Carbon, Hydrogen, Oxygen, Nitrogen ; the last, Nifr< 
being most abundant in animals. To these are added, in 
smaller proportions, Phosphorous, Calcium, Sulphur, Chlorine, 
Fluorine, Sodium, Potassium, Iron, Magnesium, Silicon. 



490 LOGIC OF BIOLOGY. 

The various properties, Physical and Chemical, belonging 
to the several elements are found operative in their organized 
form. All the mechanical and molecular laws are traceable 
in living bodies. 

tmically considered, organic bodies, are exceedingly 
complex compounds. The department of Organic Chemistry 
is devoted expressly to these compounds. According to the 
chemical reckoning, a single atom of an organic substance, as 
sugar, starch, albumen, contains hundreds of simple chemical 
atoms ; the atom of albumen is said to be made up of 880 
atoms of the four chief organic elements. 

II. With reference to Structure. 

(1) Living bodies possess a peculiar structural complexity, 
commonly called the Organized Structure. Associated with oui 
notions of life is a certain mechanism, or machinery, very 
various in its extent and complication in individuals ; attain- 
ing in the higher animals a degree of complicated adjustment 
unequalled in any other department of nature. Such struc- 
tures as the eye, the ear, the brain, of human beings are, in 
our conceptions, the very acme of structural mechanism. 

It is now known that the ultimate constituent of all the 
variety of structures is a microscope element called a cell, or 
nucleated corpuscle ; by whose aggregations and transforma- 
tions, tissues are formed, which tissues make up the organs. 
It is true that in certain low forms, both plants and animals, 
the cellular structure is not apparent, and therefore its visible 
peculiarities — namely, the bounding pellicle and internal 
nucleus — are not absolutely essential ; still, we cannot omit 
from the definition an arrangement so completely bound up 
with all living nature, the few apparent exceptions being 
equivocal. 

(2) Another prominent feature of the living structure is 
Individuality, or individuation. Living matter instead of exist- 
ing in vast continuous masses, like rock, is separated into 
distinct individuals. As with other peculiarities, however, 
there is an ambiguous margin here also. In animal life gene- 
rally, and in plant life generally, we have no misgiving as to 
individual existence ; men, sheep, forest oaks, are all distinct 
and separate. Still, a scientific definition must grapple with 
the whole field of cases, having merely the requisite latitude 
of a small doubtful margin. Mr. Spencer defines the indi- 
vidual, with reference to his definition of Life, as any concrete 
whole performing within itself, all the adjustments of internal 



LIVING STi; 

to external relations, so as to maintain il 
This definition, to a certain extent anticipa! 

5 
trnctnre and Function is one of great I 

but. in nature, the two things 

With Individuality there 
ceptions of living beings, the Cycle 
of one living being from others, and the 
of each individual's existence, after a defini 
too, we may seem to anticipate what belon< 

(3) We may not improperly state in connexion with .struc- 
ture, and as following on Individuality, a cir 
notorious, that to omit it from the comprehensive 
life would appear inexplicable, namely 
Forv Uniformity, comparatively E 

pervades dead matter; variety is the characteristic of I 
substances. The different forms of PJ 
count by thousands ; there are upwards of one ban 
thousand species of Plants, and a still greater number of 
Animal Species; while of every one of these distinct 
there is an indefinite unceasing multiplication of individuals, 
nearly, although not absolutely alike. 

One of the chief demands of Biological science is to find an 
orderly arrangement for such a host of various forms, 
makes Biology, inter alia, a science of Classification. 

III. As to Functions. 

The living structure is naturally active, changing, produc- 
tive, and its most characteristic points must hav< <-e to 
these activities. Here we may embrace the substance of Mr. 
Spencer's definition, in two principal heads — Change, 
Adjustment to external circumstances. 

(1) A definite combination of changes, simultaneous and 
successive. 

(2) An adjustment to external circumstances. 

(3) It must seem unpardonable, however, not to bring out 
into prominent statement at the outset, that very remarkable 
phenomenon of living bodies, to which there is no e 
namely, AssimilaiL », or the power of an e 

particle, to impart its own organization to an adjoining 

having the proper chemical constitution. 

of vitalitv, has only a faint parallel among inanimate j 

combustion, and chemical combinations generally, m 

small approach to it. Its le« D the 



£92 LOGIC OF BIOLOGY. 

renewal, by nutrition, of the living tissues ; its culmination 
is in the throwing off of the germ, or seed, apparently homo- 
geneous and structureless, but possessed of interior markings 
that decide whether its future is to be a man or an oak; a 
white man, or a negro ; a flat nosed or an aqulline-nosed man 
or woman. We may not be able to consider whether thi3 
great property be essential and fundamental, or whether it 
be derived from other properties, already given in the defini- 
tion. 

We may repeat under this head, the peculiarity above 
adverted to, under individuality of structure — the Cycle of 
existence, or birth, growth, and death. * 

(4) It cannot be irrelevant to the comprehensive definition 
to advert to the connexion of Mind with Living Bodies. 
True, this is not a concomitant of all living bodies, yet 'it 
appears only in connexion with the living form. When we 
make the first great division of life, into Plants and Animals, 
we obtain the more precise boundary of the mental manifesta- 
tions. Still, at the very outset, we are interested to know 
that this characteristic manifestation appears only in the 
department of living structures. 

The foregoing definition professes to leave out no fact that 
can be found inhering in all living bodies. The first requisite 
in defining is to be exhaustive ; it is an after operation, of 
great scientific interest, to trace the dependence of one or 
more properties upon the others, and to assign what appears 
to be the ultimate and underivable properties. At present, 
however, all such derivation is but tentative and hypothetical, 
and therefore, is not suitable to be brought forward at the 
commencement of the subject. Provisionally, these various 
peculiarities are to be held as distinct ; no one being assign- 
able as a derivative of another. 

Divisions of Biology. 

4. The Divisions of Biology are in conformity with the 
Definition. 

The first part of the Definition refers to the Organic Chemi- 
stry of Life. This subject is partly given under Chemistry, 
and partly as the Introduction to Biology. 

The two other parts of the definition suppose a separate 
consideration of Structure and of Function. We should fully 
understand the reasons and the limits of this separation. 






STRUCTURE AND FUNCTION VIEWED SEPARATELY. L98 



These two facts are inseparable in the reality. B 

5S complicated subjects than Life, we have often 
abstraction of some qualities to the exclusion of oth< i 
there is no actual separation possible, so in the present 
we find it advisable to consider Structure by itself, I.. 
viewing it as connected with Function. 

Yet this separation may be carried to an unjust id 
extreme. As soon as the mind has perfectly comprehend 
structural arrangement, we are prepared to enter upon the 
or functions of that arrangement. Indeed, while the know- 
ledge of the structure is still fresh, the knowledge of function 
should be imparted. Function completes and fixes the idea 
of structure, in so far as the two are manifestly conne* 
The only reason for not following up the account of structure, 
wrth the account of function, for every distinct living organ, 
would be the necessity of viewing Function as a connected 
whole, and therefore not to be entered on unless it could he 
given as a whole. For example, the Function of Digestion 
could not be entered on till the entire group of alimentary 
organs were structurally described. 

The separation of the two subjects is carried to a question- 
able extreme in the special Biology of man ; Anatomy and 
Physiology being, by present convention, treated in distinct 
works, and taught by distinct teachers in the schools. Tho 
just middle plan would be to include both in one work, and 
to append to the Anatomy of each organ — Bones, Muscles, 
Heart, &c. — the Physiology or function. 

In the usual treatment of Plant Biology, Structural Botany 
is given first, Physiological Botany next (in the same treat- 
ise) ; the student being made to wait for the account of 
Function in any organ until Structure has been gone through 
in every organ. The justifying reasons are probably these : — 
(1) It is possible to carry provisionally the whole structure 
in the mind, without the assistance that function would give ; 
and (2) there is a convenience in treating function as an un- 
broken whole. 

In Animal Biology, the branch called Comparative Anatomy 
takes each organ apart, giving both structure and function, 
and exhausting the varieties of each through the animal series. 

Structure has to be viewed, in its successive moditirat 
through the cycle of the individual life. Tliis is called 
Embryology. A still more extended view is the 
tion of successive structures in the hereditary line, where 
there may occur changes requiring to be taken accoui. 



401- LOGIC OF BIOLOGY. 

being the initial step of the new biological department called 
Evolution. 

It is proper to generalize to the utmost the wide variety of 
structures, and to exhibit all the generalities apart as giving 
a mental command of the entire field. Such generalities 
would bo c:.lled General Morphology, and General Embryology. 

Function, or Physiology, is an account of all the living pro- 
cesses, in the most convenient order ; all those changes con- 
stituting Life — changes simultaneous and successive, contri- 
buting to a definite result, and adapting each organism to the 
environment. Here there is an unlimited scope for inductions, 
and for deductions, confronting and correcting one another. 
The high generalities of Function comprehending all Life, if 
such tli ere be, would form a General Physiology. 

The subject of Evolution involves the mutual actions and 
modifications of Structure and Function. It deals with the 
general truth that when external circumstances demand and 
prompt an increase of function (as when an animal is called to 
exert unusual muscular energy) the structure is liable to be 
increased, and thus to increase the function apart from stimu- 
lation. This is one way of the supposed re-action of Structure 
and Function. Another way is by Mr. Darwin's Natural 
Selection, or Survival of the Fittest. The carrying out of these 
principles is the substance of the great Biological Hypothesis 
of Development or Evolution. 

Biology can to a certain extent be treated as a whole, there 
being certain things common to living beings — Constituents, 
Structure, Function and Evolution ; it would then have to be 
divided, as has always been usual, into Plant Life and Animal 
Life ; each of these subjects being subdivided according to the 
plan above laid down for the whole. 

Remaining Notions of Biology. 

The general definition of Life has been seen to carry with 
it the definitions of Organization, Cell, Protoplasm, Assimi- 
lation, Individual, Germ, Eejjroduction, Growth, Death. 

The specializing of the structures and functions introduces 
many other Notions. 

Plant — Animal. — The greatest line of demarcation in living 
bodies is between Plants and Animals; these are the two 
highest genera of living bodies, a perfect dichotomy of the 
whole. Allowing for a doubtful margin, the distinctive 
characters are numerous and important. As in all dichoto- 
mies, we have the advantages of a definition by Antithesis. 



PAItTS AND PROCESSES OF PIAXTS. 

'he leading characters may bo stated in contrast thus : 

Plant. Animal. 

7 umber and complexity of Tissues, Organs, and Functions. 
Small Great 

Local habitation. 
■Fixed Moveable (Locomotion) 

Food materials. 
Inorganic Organic 

Mode of reception of Food. 
Absorption Reception into a mouth 

and stomach 
Process of nutrition. 
Deoxidation Oxidation, 

Tissue. Organ. Vessel. — These are comprehensive parts or 
constituents of the organized structure, as made up of cells ; 
they are common to all living bodies, and admit of exact 
definition. There is a difference between the Tissue and the 
Organ ; one Organ, as the stomach, may contain several 
tissues. Each Tissue is analyzed into a distinct cell structure, 
which is its defining peculiarity as regards structure, to which 
there also corresponds a certain kind of activity or function. 
Thus, the nervous tissue is made up of nerve fibres and nerve 
cells, in a special aggregation ; these are connected with the 
peculiar activity or function called nerve function, or the 
manifestation of nerve force. 

The view of Plant Life contains the definitions of the 
structural -parts of the plant. 

Cellular Tissue Integument (Stomata, Hairs, Glands) 
Vessels Root 

Vascular Tissue Stem 
Leaves 

Inflorescence (Flower, Fruit, Germ). 
From the enormous number and variety of plants, a great 
effort is needed to present these parts in their widest gener- 
ality ; while the general idea must be accompanied with a 
classified detail of modifications. 

Definitions must also be given of the processes of Plant 
Life. 

Osmose Flowering 

Exhalation Vigils of Plants 

Transpiration Sexual union 

Secretion Impregnation 

Irritability and Contractility Fecundation 

Defoliation Germination 

Circulation, sap, capillarity Propagation. 

22 



496 LOGIC OF BIOLOGY. 

A set of notions, parallel but more numerous and compli- 
cated, belong to the description of Animal Life as a whole. 1 
The modifications of the ultimate materials are described as 
blastema or matrix, crystals, protoplasm, granules, homogeneous A 
membrane, vesicles, nuclei, nucleated cells, simple fibres, nucleated 
fibres, compound fibres, and tubes. These are compounded into i 
the characteristic Tissues— Cellular, Adipose, Vascular, CartU 
laginous, Osseous, Muscular, Elastic, Epithelial, Nervous. The 
Organs are Bones, Muscles, Alimentary Canal, Respiratory 
Organs, Heart and Blood Vessels, Sympathetics, Skin, Brain, 
Senses, Reproductive Organs. The Functions follow the 
Organs ; and in several instances, give these their distinctive i 
names. 

The Classification of Plants and of Animals gives scope for 
Definition as applied to the several grades. 

5. In these detailed Notions, we have the analysis of the 
Living Organism — Plant or Animal. 

An organism is by its very nature a complexity. , In a 
scientific consideration this complexity has to be resolved into 
the related parts — organs, tissues, constituents. The laws of 
structure are laws of relations of the parts to each other ; 
and if our analysis has hit the natural partition, it is the basis 
of our subsequent statements, in propositions, of the natural 
relations. If the analysis is inexact, no exacb propositions can 
be grounded on it. 

Propositions of Biology 

6. The Laws and Propositions of Biology differ in their 
logical character, according as they relate to Structure or | 
to Function. 

First, as to Structure. 

The propositions or laws of Structure, affirm co-existence, 
as order in place, between the different parts of living bodies. 
Human Anatomy is a vast congeries of such propositions. 
How far the co-existences are ultimately dependent on Causa- 
tion, rests with the theory of Evolution. In the meantime, 
they are to be regarded mainly as Co-existence without Causa- 
tion. 

These propositions may be special to individuals and limited 
groups of individuals ; or they may be generalized over very 
wide areas. The narrow class is exemplified in human Ana- 
tomy, and in all specific descriptions whether of plants or of 



PROPOSITIONS OF ANIMAL STKl < 

animals. High generalities, realizing the scientific ideal of 

Biology, are not wanting. For example, in P] 

parts are homogeneous in structure; or, as other* 

the flowers are modified leaves ; the monocotyledonous i 

of germination co-exists with the endogenous mode ol growth ; 

flowering plants are generally multiaxial ; compli 

tare is accompanied with permanence of form. In An- 

we have the anciently observed coincidence oi ruminant 

mach, cloven hoof, and horns; the grouping of mammalian 

characteristics — mammae, non-nucleated red blood-corpui 

two occipital condyles, with a well-ossified basi-occipital, 

ramus of the mandible composed of a single piece of bone and 

articulated with the squamosal element of the skull. 

Viewed, in the first instance at least, as co-existenees with- 
out causal connexion, these propositions must be veriGed by 
agreement through all nature, and held as true only to the 
extent observed. 

There are numerous and striking co-existences between 
Structure and External circumstances, the so-called Adapta- 
tions of one to the other; but in these there is a great pre- 
sumption of cause and effect ; they furnish the best support to 
the doctrine of Evolution. 

There are likewise laws of causation, more or less traceable, 
m the operation of all the outward agents. Thus, Hear, 
Light, Air, and Moisture, are essential or causal conditions of 
the growth of plants. Light is necessary to the colour of the 
leaves. The oxygen of the air is an indispensable condition 
of all animal life. Many other laws of causation are occupied 
in expressing the agency of different kinds of food, of medi- 
cines, &G. 

There are laws of cause and effect, in the mutual actions of 
different organs, in each individual plant or animal. Thus, 
in animals, the digestive organs affect, and are affected l<y 
the circulation, the muscles, and the brain. 

7. Next as to Function, or Physiology. 

The propositions here affirm Cause and Effect. The pri 
of Digestion, for example, is an effect of the contact of lo«»d 
material with the complicated alimentary organs. in 
manner, every organ of every living being has a fane 
more or less assignable. 

It is a deduction from the permanence of Matter, established 
since the researches of Lavoisier as 4 a law of nature, that what- 
ever materials exist in plants and in animals, musi 



408 LOGIC OF BIOLOGY. 

plied as a condition of their growth. Plants being constituted 
from Carbon, Oxygen, Hydrogen, Nitrogen (in small portions), 
and Saline bodies, — must find all these elements in the earth 
or in the air. The animal tissues being highly nitrogenous, 
animals must have nitrogenous food. (_The gastric juice con- 
tains hydrochloric acid, whence the necessity of salt as an 
article of food. 

8. The law of the Conservation of Force, and all the 
subordinate generalizations of Molecular Physics and 
Chemistry, are carried up into Biology. 

The law of Conservation holds true in organic changes, and 
is a deductive key to the phenomena. Every manifestation 
of force in a living body — mechanical energy, heat, decom- 
position of compounds, — is derivable from some prior force of 
exactly equivalent amount. 

The laws of Cohesion, Adhesion (in all the forms — Solution, 
Capillary Attraction, Diffusion, Osmose, Transpiration), Heat, 
Light, Electricity, and the laws of Chemical combination and. 
decomposition, are carried up into organic bodies. In the 
present advanced state of knowledge respecting these laws, 
there are many deductive applications of them to the pheno- 
mena of life. The complications of Biology are thus, in part, 
susceptible of being unravelled by pure deduction. 

So far as concerns Force, or energy, in any shape, there is 
nothing special to living bodies. As regards Collocation, 
there is the peculiarity of the organized structure. It is not 
correct to speak of Vital Force in any other sense than the 
molecular and chemical forces, operating in a new situation, nj 
It would be strictly proper to speak of a Vital Collocation of 
elements, under which the molecular forces put on new 
aspects, although never inconsistent with the primary law of 
Conservation. Thus the nerve force is something new, not as 
regards its derivation from an antecedent equivalent of force, 
but as regards the singularity of the nerve structure, which' 
leads to a new mode in the manifestation of the force. 

9. In the department of Function, there are necessarily * 
many Empirical Inductions. 

Excepting the deductions from Physics and Chemistry, j 
every law of Biology must be considered as empirical. There J 
are, however, some empirical laws established by an agree- i 
ment so wide and sustained that they are considered, for the f 
present, as laws of nature. Still, no such laws can be held as 1 



PROPOSITIONS OF FUNCTION. 

absolutely certain. Notwithstanding the agreen 

at' the derivation of living beings from germs or seed, bb 

vet a possibility of spontaneous generation. 

The following are examples in Plants. Vegetable i 
ibsorb fluids, elaborate secretions, and form now ccIIh; 
also unite to form vessels. Roots absorb material from 
soil, in part by osmotic action. The sap circulates under the 
influences of heat and light, and the actions going on al 
surfaces of the leaves and of the roots. In flowering pi 
reproduction is performed by the accessor the pollen i 
ovules. Fruit succeeds to fecundation. Seeds germinate in thu 
presence of heat, moisture, and air, with absence of light. 

There is something very unsatisfactory in the inductions of 
Vegetable Physiology. Some of them are now obvious results 
of the law of Conservation ; as for example, the influenc 
Heat at all stages of vegetable growth. The great lack is in 
the intermediate steps of the process ; what happens in 
interval between the incidence of heat and air in the lei 
and the elaboration of the sap, the setting free of oxygen, Ac. 
But this is the defective part of our knowledge of all the 
organic processes. 

In the functions of Animals, there are numerous empirical 
inductions. Thus the conditions of Muscular contractions are 
well known by experimental research ; they are the presence 
of blood, and the stimulus of the nerves. That blood should bj 
necessary is a consequence of the law of conservation; muscular 
force must be derived from some prior force. That non-azol 
materials are sufficient for causing muscular energy could be 
known only by experiment. Again, the circumstances affecting 
the heart's action, are empirical inductions ; so is the (act 
that the red corpuscles of the blood carry the oxygen for tho 
tissues. The processes of Digestion are stated in the form of 
empirical inductions. The same holds of Urination and In- 
spiration. Farther, the multiplied actions concerned in 
Impregnation, Germination, and Growth, are ascertain 
only as empirical laws. All the functions of the Brain 
the Senses are given in propositions of the same characte 

That exercise (within limits) strengthens all 
organs has long been established as an Empirical Law. Mr. 
Darwin is dissatisfied with the physiological reason or deriva- 
tion of the law; to him, therefore, it remains empirical 

These empirical inductions are to a certain small ex! 
controlled by high generalities, and arc in so far derivative. 
The law of Conservation is a check upon many of them ; and 



500 LOGIC OF BIOLOGY. 

the special laws of Molecular Physics and of Chemistry arc J 
at work in some. But in such a process as Digestion, the t 
recognized physical and chemical actions are thwarted bj 
deeper forces, of which we have only an empirical statement. 
The most potent instrumentality of deductive explanations ai 
present known is that furnished by the researches of Graham 
on Transpiration, Diffusion, Osmose, and Capillarity. 

Animal Mechanics, and the propulsion of the fluids by the 
heart's action, are susceptible of a complete deductive treat- 
ment, through the applications of Mechanics and Hydrostatics. 
This is well exemplified by Dr. Arnott, in his * Elements oi 
Physics/ 

Logical Methods of Biology. 

10. In Biology, the facts are open to Observation and 
to Experiment ; although with some limitation owing to ] 
the peculiarities of the living structure. 

The difficulties attending the observation of living beings i 
are greatly overcome by such instruments as the microscope, I 
stethoscope, laryngoscope, ophthalmoscope, &c, and by the I 
chemical examinations of the various products. Accident! 
sometimes lays open the interior, as in the case of Alexis St. j 
Martin, through whom was obtained invaluable results as to I 
digestion. 

11. Through the variety of the cases presented by Biologv, 
there is great scope for elimination by the methods of] 
Agreement and Concomitant Variations. 

The means of varying the circumstances by the comparison 
of instances, agreeing and yet disagreeing, is very extensive. | 
From the number of different vegetable and animal species, j 
each structural peculiarity is presented under the greatest! 
possible variety of accompaniments. And this is only one part 
of the case. In every individual there is scope for additional 
comparisons in the different stages of its existence, the method 
of Embryology. Lastly, the occurrence of monstrosities still 
farther contributes to the desired variation of circumstances. 
In these three ways, the opportunities of plying the Methods 
of Agreement and Concomitant Variations are exceedingly 
multiplied. 

Thus, an examination of the structure of the eyes, in their 
rudimentary types in the lowest animals, and in their succes- 
sive phases of growth in the higher, has both suggested and 



CHANCE AND PROBABILITY. 

proved (as some believe) that au eye is a modified poriio 
the skin. 

Mr. Owen enumerates seven, different modes of carrying 
comparisons of the animal structures (Vertebrate \ 
Vol. I. Preface). 

The nse and limits of the Deductive Method In Biology I 
been sufficiently adverted to in previous remarks. g 
notice may be taken of the applications of Chance and 1*1 
bility. 

12. There are many biological conjunctions of wide, 
but not of uniform concurrence. Such cases must be dealt 
with according to the rules for the Elimination of Chance 

When a concurrence, although not universal, is, neverthe- 
less, more frequent than chance would account for, we aro 
bound to recognize a natural tendency, or some law of nature 
liable to be defeated by other laws. For example, the con- 
currence of superiority of mental power with superior size of 
brain, although liable to exceptions, is yet very general, and 
far more than chance can account for. Hence we must regard 
this as an established law, with occasional liability to be 
defeated. We are not at liberty to predict it of every instance, 
but only with a probability proportioned to the observed fre- 
quency as compared with the failures. 

13. It is a result of the great complicacy of vital pro- 
cesses, that many inductions are but approximately true ; 
and, therefore, are to be reasoned on according to the 
principles of Probable Evidence. 

The prevalence of approximate generalizations is a mark of 
the increased complicacy of the Biological processes, as com- 
pared with the processes in Physics and in Chemistry. 

The best that can be done, in this state of things, is to ob- 
tain statistics of the actual occurrence of certain conjunctions. 
There is a large department, of modern creation, termed Vital 
Statistics, which enables us to reason on vital phenomena with 
the degree of probability belonging to each case. It is thus 
that we can infer the proportions of mortality at different 
and the proportion of male to female births. When Agriool* 
tural Statistics shall have been continued for a suilieient time, 
the recurrence of good and bad harvests will be capable of 
being stated with numerical probability. 

14. Many of the propositions of Biology are defective in 
numerical precision. 



502 LOGIC OF BIOLOGY. 

In Physical and Chemical facts, it is usually possible to 
measure numerically the degree of the qualities. Thns most 
of the properties of a mineral can be stated with numerical 
precision ; others, as colour, and fracture, can be referred to 
a known type. But when we say a certain amount of exercise 
strengthens the organs, while a greater amount weakens them, 
we leave the estimate very vague. Change of air is said to 
invigorate the powers, but there are no precise reckonings, 
either in the general or in particular cases, of how much invi- 
goration may be expected from a definite change. So, the 
influence of altered circumstances on breeds and on races is 
given in vague indeterminate language, and must be taken 
with great latitude. 

Hypotheses of Biology. 

15. The character of the science requires the utmost 
aids that can be afforded by well-contrived Hypotheses. 

Biology has all the difficulties of Molecular Physics and 
Chemistry as regards the impalpable nature of the constituent 
parts in living bodies, and its own additional complications 
from the organized structure. 

The hypotheses of Biology are of all the varieties enu- 
merated in the general chapter on the subject (Induction, 
chap. XIII.). Some assume a real cause, as the Development 
Hypothesis ; others assume unreal or unknown agencies, as 
the supposed adherence to Type or plan; a third class would 
claim to be Representative assumptions. 

Of the first class, we may cite, as instances involving the 
smallest amount of peril in the assumption^ the unverified 
deductions from general laws of the inorganic world, such as 
the molecular and chemical laws. These powers of cohesion, 
adhesion, solution, osmose, &c, are assumed as operating in 
the living body, but the deduction from them is not sufficiently 
exact to be fully verified. Hence there is much that is hypo- 
thetical in the theories of oxidation, of animal heat, of secre- 
tion, &c. From the known chemical inertness of Nitrogen, 
Mr. Herbert Spencer draws some remarkable inferences in 
explanation of the vegetable and animal processes (Biology, 
I. 8). 

Development Hypothesis. — This renowned speculation, with 
all its boldness, has the characters of a legitimate hypothesis ; 
it assumes a real agency, a vera causa ; its difficulties lie in 
showing that the supposed agent is equal to the vastness of 
the results. 



HYPOTIII 

Properly speaking there is no rival hypothesis. T 
ition view is a phrase; 

t of explanation is confined to i 
ssigns to the living species that hav 
in the course of ages the same mode i 
ies of all, and as the whole framewn 
a that mast for ever be inconceival 
As the physical theorists who speca 
ment — the formation of suns and planets— e< 

nption of matter spread out over 
space, and coming together by gravity, so the bi 

assume a primeval start, either of li. 
matter ready to become organized under particular cir 
stances. Now the value of any scientific explanation of I 
measured by its capability of tracing the whole of o 
nature to the fewest primitive assumpti 

The modification of plants and animals in the course of 
generations is a fact. It happens even in the - 
ciix'umstances ; while under alteration of circu s, the 

changes become vastly greater. Now, if any : tan bo 

ned whereby some of the modified forms are 1: 
while all the others perish, the deviations are rem. 
manent. Mr. Darwin provides an instrum ntaliry of this 
nature in what he calls Natural Selection, or the preserv 
of the fittest in the struggle of life. It has been his ei 
to accumulate a vast multitude of facts showing the principle 
in operation, many of them inexplicable on any i 
tion. Herbert Spencer, Huxley, Hooker, Walla 
have contributed to the support and elucidation of I 
thesis. 

The occurrence of allied species in the same 
area, and the wide differences in c 
localities widely apart, are adapted to the doc 
lopment and not to any other view as yet provi led. Ag 
savs Mr. Darwin — 'How inexplicable is the similar p 
the hand of a man, the foot of a dog, the v. b, tho^ 

flipper of a seal, in :trine of indi 

creation ! how simply explained on the | 
selection of suce 

descendants from a single progenitor! 1 1 
time and change, certain parts originally n 
superfluous; and their retention in the 
intelligible onlv on a hypothesis 

So long as the J 



504 LOGIC OF BIOLOGY. 

large number of facts, and is not incompatible with anj, it is 
a legitimate and tenable hypothesis; and its worth is propor- 
tioned to the extent of the phenomena that it explains, com- 
pared with those that it foils to explain. 

Hypothesis of Reproduction. — The reproduction of each living 
being from one or from two others, through the medium of a 
small globule which contains in itself the future of a definite 
species, is the greatest marvel in the whole of the physical 
world ; it is the acme of organic complication. 

Mr, Herbert Spencer and Mr. Darwin have recently pro- 
mulgated hypotheses to represent this process. (Spencer, 
Biology, I., 253 ; Darwin, Domestication, II., 357). The two 
views have a good deal in common, and might be taken 
together. Mr. Darwin's, however, ventures farthest, and 
may be here quoted as exemplifying a biological hypothesis. 
He prepares the way by generalizing all the different modes 
of reproduction — whether unsexual or sexual. The unsexual 
modes, as buds and fissure, are to be held as identical with 
the processes for maintaining each organ in its integrit} 7 , for 
the growth or development of the structure, and for the 
restoration of injured parts. And it seems to be a tenable 
supposition that the sexual mode of reproduction is a mere 
modification of the same general fact. 

The hypothesis then is that each egg, or seed (of the female) 
and each spermatozoon, or pollen grain (of the male) is already 
a vast aggregation, a world in itself. It is made up of a host 
of smaller bodies, which may be called gemmules, with all the 
properties of growth or reproduction commonly attributed to 
cells in general ; this host is different in each species. For 
every separate part of the animal or plant to be formed, down 
to a feather, there are distinct gemmules of the type of that 
part, and unfolding to produce it by ordinary growth. Every 
animal contains circulating through it the undeveloped gem- 
mules of all its organs, and parts of organs ; a complete set is 
bound up in the ovum of the animal (or plant), and by due 
expansion reproduces the new individual complete at all points. 
Something must be assumed as determining them to fall into 
their places; but that there is no absolute fixity in this respect, 
Mr. Darwin shows by the frequent occurrence of misplaced 
organs ; this, he thinks, favours the view of the multitudinous 
gemmules, and refutes any hypothesis of a formed microcosm 
existing in the seed, to which supposition there are many other 
hostile facts. 

To grasp, reconcile, and generalize the. facts, is an ample 



HYPOTHESES. 



stification of this bold venture; by tho nature of the i 
we can never hope to penetrate the precise operation, 
to arrive at a supposition that shall exclude every other. * It! 
is, however, an important appendage to whatever byppl 
may be formed of the great vital fact named Assimilation. 



CHAPTER V. 
LOGIC OF PSYCHOLOGY. 

1. Psychology, or the Science of Mind, comprises both 
Mind proper, and its alliance with Matter, in the animal 
body. 

Definition of Mind. 

2. The ultimate antithesis of all knowledge is called the 
antithesis of Object and Subject. 

The object world coincides with the property called Exten- 
sion ; whence the Subject, or Mind, is definable by antithesis 
as the Unextended. A tree is extended ; a pleasure, a though^ 
a desire, have nothing in common with extended things. 

3. By the method of Particulars, Mind is definable as 
possessing the three attributes named Feeling, Volition, 
and Intellect. 

Feeling is exemplified by pleasures and pains ; Volition is 
action prompted by Feelings ; Thought, or Intellect, contains 
the processes known as Memory, Reason, Imagination, &c. 

All our emotions are included under Feeling ; our sensa- 
tions are partly Feelings and partly Intellectual states. 

The positive definition of the Mind is also a Division, and 
must conform to the laws of Logical Division. 

Concomitance of Mind and Body. 

4. To the Definition of Mind, we must add the Con- 
comitance of the Body. 

The concomitance of Mind and Body is a conjunction alto- 
gether unique. The extreme facts of human experience — the 
subject and the object, mind and extended matter— are found 
in union. We cannot say with certainty whether the union is 



506 LOGIC OF PSYCHOLOGY. 

a case of causation, or a case of co-inheiing attributes. It 
stands apart. 

5. The union of Mind and Body must hold throughout. 

While many, from Aristotle downwards, have held that 
portions of the mind are unconnected with bodily processes, 
no one denies that mind is to some extent dependent on the 
body. But all have failed in every attempt to draw a line 
between the functions that are dependent, and those that are 
supposed independent of bodily organs. 

6. The concomitance of the two radically distinct 
phenomena gives the peculiar characteristic of the science. 
Every fact of mind has two sides. 

Every feeling has its mental side known to each one's own 
consciousness, and its physical side, consisting of a series of 
physical effects, some superficial and apparent, others deep 
and intricate. 

It depends upon circumstances whether, and how far, these 
physical adjuncts should be brought forward in the scientific 
exposition of the mind. On the one hand, if they are 
unvarying in their concomitance, they can hardly be excluded 
without impairing our knowledge of the mental part. On 
the other hand, it is a bare possibility that the mental pheno- 
mena, being radically distinct and unique, may be studied 
better by making entire abstraction of the physical accompani- 
ments. Moreover, much depends upon the degree of insight 
actually possessed respecting the nervous system and the 
various organs related to the mind. It might be expedient at 
one stage of knowledge to drop these from the view, and at 
another stage to take them up. 

In point of fact, until the present century, only a very small 
number of philosophers gave systematic attention "to the 
physical implications of mind ; the chief being Plato, Aristotle, 
Hobbes, and Hartley. In spite of the crudity of their know- 
ledge of physiology, they all (with perhaps the exception ot 
Plato) gained most valuable psychological hints by means of 
that knowledge. The physiology of the present century 
having placed the whole subject on a new vantage ground, 
the attention to the physical side may be expected to be much 
more rewarding. 

Thus, on one side, Psychology is a department of Animal 
Biology, and subject to biological laws. The all-pervading 
law of Persistence of Force extends to the physical concomi- 



DEFINITION OF MENTAL PRO PARTIES. 

feints of mind, and is pregnant with i of tho 

* utmost practical value. 

On the other side, Psychology presents a unique phen 
non— individual self-consciousness— to which thei 
forerunner in any of the previously enumerated 
Still, the methods and spirit of scientific enquiry, a 
in these other sciences, are of value in the study of mind in 
its psychical side. States of consciousness hav< 
intensity and duration; they are single or compound 
aid or thwart one another ; they have their laws oi 
increase, decline; in all which particulars tfa 
analogies to physical forces ; so that the intellectual habil 
accurately estimating physical agencies may, with due all 
ances, be of service in dealing with the complications of mind. 

The two-sidedness of the phenomena appears in langa 
The terms of mind had all an objective origin; ami, ""while 
some of them have now an almost exclusively subjective 
meaning — as pleasure, pain, feeling, thought, sweetness, t 
conscience, remorse, — others have also an objective reference, 
as shock, emotion, excitement, avidity, irritation. In t! 
last, the language is ambiguous ; we cannot always I 
whether the physical or the mental is aimed at. There is, 
morover, a liability to represent the mental fact as a physical 
fact. 

Other Notions of Psychology. 

Consciousness. — The most difficult word in the human v 
bulary. It concentrates in itself all the puzzles of metapbysi 
If it were strictly synon} r mous with Mind, it would be defined 
accordingly. But the object, or extended world, is inseparable 
from our cognitive faculties; so that a word that ex] 
every conscious state whatever is wider than mind, strict 1\ 
called; it comprises both matter and mind. Hence, if 'con- 
sciousness ' be the name for all sentient states, it is the wi<! 
word that we can employ, in fact, there is no meaning cor 
sponding to it ; like Existence, it is a fictitious addition <>t tho 
two highest genera. To state these separately, we mn 
the double epithets Subject-consciousness and I >n- 

sciousness ; which, however, give only the meanin 
and Subject. 

Sensation. — A word with several distinct meanings. In tho 
first place, it may either cover the physical operation 
nected with the exercise of our senses, or it may b I 

to the purely mental state arising therefrom. In the nest 



50S LOGIC OF PSYCHOLOGY. 

place, inasmuch as the senses give us feelings in the purest $ 
form (pleasures and pains) and also intellectual discrimina- ' 
tions, the ground work of our ideas, — sensation may be used 
for either class. In the third place, there is a contrast of 1 

sation with Perception, or between the immediate effect 
on the mind, and the associated effects ; colour and visible 
magnitude are sensations, distance and true magnitude are 
perceptions. 

The special modes of sensation, together with muscular 
feeling, are ultimate states of the mind, to be defined solely 
by individual reference. Resistance, Motion, Warmth, Diges- 
tive Sensibility, Taste, Smell, Touch, Hearing, Sight, — as 
states of feeling:, must be known by independent experience. 

Emotion. — The emotions are a department of the feelings, 
formed by the intervention of intellectual processes. Several 
of them are so characteristic that they can be known only by 
individual experience ; as Wonder, Fear, Love, Anger. These 
stand very near the ultimate elements of human feeliner. 
Many, however, are evidently derived ; such are, in an emi- 
nent degree, the ^Esthetic and the Ethical emotions. 

Phases of Volition. — The definition of the Will, or Volition, 
is a part of the definition of mind as a whole. Will, as con- 
trasted with Feeling, is a unity, indivisible. Yet, there are 
various aspects or modifications of it, that receive names. 
Motive is the feeling that prompts the will in any one case ; 
the motive to eat is the pain of hunger, or the pleasure of eat- 
ing, or the pain of defective nutrition. Deliberation supposes 
conflicting motives. Resolution is a volition with the action 
adjourned. Desire is ideal volition, either as preparatory to 
the actual, or in lieu of it. Belief is preparedness to act, 
for a given end, in a given wav. 

Intellectual States.— In the" Intellect, we have three fun- 
damental processes — Discrimination, Similarity, Retentiveness 
or Revivability ; all requiring actual experience in order to be 
understood. Discrimination^ anotherword for the fundamental 
fact called Relativity and also Contrast. Similarity, or agree- 
ment in difference, is a distinct fact of the mind ; the sensi- 
bility corresponding to it is unique ; and it is one of the most 
iterated of human experiences. Retentiveness and Revivability 
describe a great characteristic of our mental nature, for which 
we have other designations, as Idea, Memory, Recollection ; it 
can be defined only by reference to actual experience ; al- 
though the figurative words— retention, revival, resuscitation, 
seem to be a definition bv the medium of other notions. 



ESSENTIAL AM) REAL PBKDH 

The complex intellectual faculties— 1 
&c, are defined each by its proper department of - • 

thus, Reason is the power of drawing conclusii 
mises, or the scientific faculty. To this definition m 
appended, as a real predicate, the derivation from the 
intellectual elements just named. 

Psychology contains scope for Classification, both according 
to Logical Division, and according to Ramificati mpo. 

sition. The ultimate sensibilities— namely, the . the 

elements of Intellect, and the Simple Emotions — arc clae I 

as genera and species, and according to Logical Divi 
The compound faculties and sensibilities, as the popularly 
named Intellectual Powers, and the Complex Emotion 
classified solely by Ramification; their classes do not comply 
with Logical Division. 

Propositions of Mind. 

7. The complexity of many of the Xotions of Mind 
gives rise to Essential Predications. 

Mind itself being defined (positively) by the union of three 
distinct and irresolvable characteristics, there may be proposi- 
tions affirming the concomitance of these three facta ; as 
Feeling is accompanied with Volition and with Intelligence. 
When we say that Mind (as a whole) feels, wills, remembers, 
we give a verbal or essential predication. 

So with many other notions. Such simple feelings as fear, 
love, anger, if defined, would have a plurality of circumstai 
That such circumstances are united, may be a real predica- 
tion ; but when any one of them is predicated of the name, 
the proposition is essential. * Anger makes one delight in 
retaliation ' is a purely verbal predication. 

Our common talk on mind is full of Essential propositions. 
His vices were condemned, his virtues praised. Prudence 
keeps a man out of difficulties. The strongest motive deter- 
mines action. 

8. The conjunction of Mind and Body is a real predi- 
cation ; it being understood that the definition of Mind is 
restricted to subjective facts. 

This holds throughout the detail of feelings, volitions, nnd 
thoughts. When the name for an emotion is the su 
proposition, and the physical accompaniments are alii: 
the predication is real : — ' Fear depresses the vital organ 



510 PSYCHOLOGY OF LOGIC. 

an affirmation of concomitance. l The hope of the reward 
quickened bis speed ' conjoins a motive to the will (a feeling) 
with the bodily part of a voluntary act. 

9. The three leading functions, given as the Definition 
of Intellect (Discrimination, Agreement, lietentiveness), 
are unfolded in predications. 

That Mind discriminates is an Essential proposition ; yet the 
fall account of the fact of Discrimination, Relativity, or Con- 
trast, demands numerous propositional statements, many of ; 
them real. Not to re-iterate the double-sidedness of every 
mental fact, the conditions, circumstances, and limitations of , 
each of these leading properties are enounced in propositions 
that are in no sense verbal. 

(1) Thus, we speak of the law of Relativity, expressed as 
the concomitance of consciousness with change of impression. 
This is the general statement ; and constitutes a real predication 
by virtue of the distinctness of the two facts — change of im- 
pression (physical, in great part), and consciousness (strictly 
mental). 

(2) Retentiveness, II evlv ability, Contiguous Association, are 
names for a fundamental property of mind, which in its expo- 
sition takes the form of a law. A certain condition or situa- 
tion has to be assigned (the reception of present impressions), 
and to this is attached as a real predicate, the property of 
be'ing retained, revived, remembered. The various modifying 
circumstances (engagement of attention, physical vigour, &c.) 
are real propositions in subordination to the main principle : 
It is a grand generalization, resuming, explaining, and ren- 
dering precise the media axiomata of acquisition, as regards 
intellectual growths, emotional growths, and volitional growths, 
Under it are given numerous affirmations as to the derivation 
of complex phenomena from simpler, the unfolding of thoughts 
and emotions, and the evolution of the mature mind from its 
primary elements. This is commonly called the Analysis of 
the Mind. The proof of such assertions rests partly on the 
consciousness of the hearer, and partly on indirect reasonings. 
Thus, the proof that Beauty is a compound, and not a simple 
Emotion, is that we can consciously identify its constituents. 
The same with the Moral Sense. The indirect proofs are, the 
absence of the Feeling prior to certain opportunities of mental 
association. (See § 12.) 

(3) The Law of Similarity, or Agreement in Difference, is, 
for the same reasons, an inductive generalization of real 



LAWS OF KIND. ;, J J 

concomitance. ' Present states of feeling & 
their like among former states, notwithstandii 
amount of difference.' As before, ther [aired i 

subsidiary propositions to express all the quali 
■tances of this wide generality. 

Another important law of the mind is sol- 
as the law of the Fixed Idea, namely, that ideaa tend to 
themselves out ; as when the sight oi' yawning m 
merely by giving us the idea of the act. 

10. There may be laws of the rise, continuance, and 

subsidence of Feelings. 

o 

The connotation of each distinct mode of feeling, wli 
sensation or emotion, indicates both its character as feeling, 
and its mental antecedent. The laws connecting mind and 
body, predicate its physical side; the laws of Relativity and 
of Ketentiveness contain additional predicates. To all these 
may be added inductions as so the rise, continuance, and 
sidence of Feeling ; which laws, like every other, have a phy 
side, and may possibly, on that side, be generalized into still 
higher laws. 

Like all sciences where simple elements contribute to form 
compounds, Psychology contains affirmations respecting the 
composition of feelings and other states. The assertion is 
made, for example, that Beauty, Conscience, Imagination, are 
not simple facts, but are compounded of certain assignable 
elements. 

Among the ordinary predications respecting livin 
we may mention the passing of the various capabilities into 
action. This extends to mind. I walk, speak, reason, wonder, 
desire, &c, are examples; to all such belongs the real. 
predication. 

Logical Methods of Psychology. 

11. In Psychology, special importance I to the 
ultimate Analysis of the phenomena. 

In all sciences, we desiderate an accurate and thorough- 
going analysis of the phenomena. It is only an ultimate 
analysis that can be the groundwork of the most general pre- 
positions respecting them 

In proportion to the difficulty of ascertaining and proving 
the facts in detail, is the value of an ultimate analysis, irhe 
we can reduce to a minimum the number of independent 



512 LOGIC OF PSYCHOLOGY. 

assertions. When we know the component parts of an Emo- 
tion, for example, Beauty, the Moral Sentiment, or Veneration, 
we can apply our experience of the parts to correct and con- 
firm our experience of the totals. 

12. The proof of a Psychological Analysis is (1) the 
feeling of identity between the compound and the parts. 
This must be a matter of individual self-consciousness. 

That the Moral Sentiment contains a feeling of obedience 
to authority, under dread of punishment, is proved by each 
one's being conscious of the presence, in the compound, of 
that special element. 

13. An Analysis is proved (2) by the identity of the 
consequences and collaterals of a feeling. This will 
afford an Objective proof. 

That the Religious Sentiment contains an element of Fear, 
is proved by identity in the Expression and the Actions 
dictated by the state. 

14. The greatest difficulty is felt in establishing the 
sufficiency of an Analysis. 

This is a difficulty in all cases .where there is great com- 
plexity in the phenomena. We may identify the presence of 
certain elements, without being able to show that these are 
the whole. Where the quantity of the elements can be 
measured, as in Chemistry, we can prove the analysis by 
casting up their sum. Where quantity is not exactly esti- 
mable, as in many biological facts, and in nearly all psycho- 
logical facts, this check is indecisive. 

For example, some have maintained that Benevolence is 
exclusively made up of self- regarding elements. Others, 
while admitting the presence of these elements, deny that 
they account for the whole. Owing to the vagueness of our 
estimates of quantity in mind, the dispute cannot be decided 
by a process of summation in ordinary cases. We must 
proceed by varying the circumstances, and by finding 
instances where self-regarding elements are either wanting, or 
so small in amount, as to be obviously unequal to the effect 
produced. Such an instance is found in the pity called forth 
by the punishment of great criminals. 

15. The Inductions of Mind bring into play the Experi- 
mental Methods. 



LOGICAL METHODS IN Mi 

The great Law of Concomitance of Mind and D 
proved by the Method of Agreement. We ma 
the whole of the facts of mind— Feelings, Volitions, Thou 

are at all times accompanied by bodily pr< 
has something of the peculiar; 

We can prove the concomitance in a vast number * 
while in many mental exercises, as in meditative reflection, 
the physical processes almost escape detection from 
subtlety. These instances, however, although unable to 
confirm the proposition, are not opposed to it ; and they 
do nothing to invalidate the force of the unequivocal in- 
stances. 

We can do more than establish a law of concomitance of 
mind and body generally. We can, by the methods of Elimi- 
nation, ascertain the exact bodily processes connected with 
mental processes. On this determination, we can bring to 
bear all the Experimental Methods. 

The Law of Relativity is established by Agreement, and, in 
a remarkable manner, by Concomitant Variations. 

The Intellectual Laws, called Retentiveness and Similarity, 
are established, both in general terms, and as respects 
peculiar conditions, by all the methods. 

16. From the circumstance that, in Psychology, we have 
attained to laws of high generality, there is great scope for 
the Deductive- Method. 

While every one of the great laws above enumerated is 
fruitful in deductive applications, the instance that perhaps 
best exemplifies the Deductive Method of enquiry, considered 
as a supplement to Induction, is the Law of Conservation or 
Correlation, applied to Mind, through the physical supports. 
By this law, every mental act represents a definite, although 
not numerically expressible, physical expenditure, which must 
be borne by the physical resources of the system. The d< 
tive consequences of this fact are innumerable. A few 
instances may be briefly suggested. Great mental labour or 
excitement is accompanied by corresponding physical v>. 
which is so much subtracted from the total of the phj 
forces available for the collective neec 

Again, great expenditure in one mode of mental exertion, if not 
at the expense of the more properly bodily fund I the 

expense of other mental functions ; and so on. No* 
cases, we may apply the deductive process, in all it- 
there is a prior Induction, there may be a process of Culcula- 



514 LOGIC OF PSYCHOLOGY. 

tion so far as the case admits ; there should be a Verification, 
botli from isolated tacts and from empirical laws. 

These Deductive applications are a valuable check upon the 
loose empiricisms so abundant in the treatment of mind, and 
are the best testimony to the use of a science of psychology, 
in spite of its imperfections. There are empirical generaliza- 
tions on the points just alluded to, namely, the incompatibility 
of great expenditure in one direction of effort, with great 
expenditure in other directions. Now, by the Law of Conser- 
vation, such empiricisms receive their definite limitations, and 
the exceptions are fully accounted for. 

17. The Psychological mystery of the union of Mind 
and Body is the severest test of logical Explanation. 

Enough was said in this head, under the chapter relating to 
Explanation. 

Empirical and Derivative Laws in Mind. 

18. There are in Mind many Empirical Laws, but, as a 
consequence of the attainment of high generalities, there 
are also Derivative Laws. 

From the complication of the physical adjuncts of mind, 
considered as the culmination of Biology, we may expect 
many of the Inductions to be purely empirical, and as such 
narrowly limited in time, place, and circumstances. 

The phenomena of Dreaming can be stated only as Empirical 
Laws, with a certain aid from hypothesis. 

We have only pure empiricisms to express the operation of 
stimulating drugs upon the emotional states ; whereas the 
laws that state the operation of food or mutriment can be 
derived. 

Hence, a very great number of the inductions of mind may 
be traced as Derivations of these higher laws, whereby they 
attain a greater certainty and compass of application. All 
the rules for aiding memory are easy deductions from the 
great law of Retentiveness. The effects of Novelty, and Con- 
trast, are derived from the Law of Relativity. 

Strictly speaking, the supreme laws of mind— Relativity, 
Retentiveness, Similarity, &c, are but a high order of em- 
piricisms. They are not ultimate laws of nature, like 
Gravity and the Persistence of Force. They are, however, 
exhaustively verified through the whole of mind ; and are 



HYPOTIIK 






applicable in accordance with the extent of ihei 

A\ e properly treat them as the highest or q] 

department, and employ , out 

derivative laws. 

Hyp ' s n Mind. 

19. The principal exam 
seuse, are to be found in the great pi 
namely, Innate Ideas, External Perc 

Perhaps the instance most in point is .on. On 

subject, there prevails the assumption of an indepen 
material world and a series of independent minds, bn 
into mutual contact ; an assumption that has fch 
mendation of easily and simply expressing all : 

phenomena. It has, however, the serious drawback 
self-contradictory ; whereas the view that avuids the 
tradiction is lumbering and unmanageable in its j ,n to 

express the facts, and hence the backwardness t 
a substitute for the other. 

This is an extreme case of a hypothesis believed solely be- 
cause it squares with the appearances. Xot only i.^ there an 
absence of proof otherwise, but there is flagrant self-co: 
diction, which ought to be considered as a complete 

Among the unexplained phenomena of rniad, we are to in- 
clude Dreaming. One hypothesis on this subject is a real 
cause, namely, the partial activity or wakefulness of the b 
It is a fact well established that the brain may be either alive 
or dormant in all degrees. Now if we assume wakefulm 
certain parts, and dormancy in others, we may account for 
many of the appearances of dreaming, sonnambulism, and 
mesmerism. The hypothetical element is the selection of the 
parts, namely, the senses, and the centres of volunt;r 
ment. The coincidence of the facts with what would f 
on this assumption is a considerable probability in favour i 
hypothesis. 

It is a well-known fact that when a chain of ideas has often 
passed in succession, and when the last link oi 
more important than the intermediate links, we | 
from the first to the last, the others not appearing in c<>n- 
ness at all. The oblivion has been the occasion ( 
hypotheses. (1) According to i . the intermeo 

are passed so rapidly as to be forgotten. 
Hamilton, it belongs to the class of latent mental | 



516 LOGIC OF CHARACTER. 

(3) According to J. S. Mill, there is a direct association formed 
between the first and the last, and the others disappear alto- 
gether from the chain. All the three suppositions refer to 
real agencies; all might operate in the case supposed. Con- 
sequently, the decision turns upon whether the effect of any 
one is exactly equal to the effect observed. Allowing for the 
standing difficulty of computing mental forces, we may say 
that, on the whole, the last most nearly coincides with the 
phenomenon. 

The exact character of the human mind at birth is a hypo- 
thesis of the second class of scientific hypothesis, a fictitious 
representation that has no groundwork but fitness to express 
the subsequent manifestations. 

The minds of other human beings and of animals are con- 
ceived by us hypothetically as expressing the appearances upon 
the analogy of our own conscious experience. 

Chance and Probability in Mind. 

20. The complications of the phenomena of Mind pre- 
vent us from attaining laws of universal application. In 
many instances, we must state our propositions as more 
or less Probable. 

The influence of Education is not in all instances certain. 
The Law of Eetentiveness is sure in its operation, but its 
various complicated conditions may not always be complied 
with. A training in good conduct, in most cases, but not in 
all, makes a good moral character ; a training in vice is 
generally, but not uniformly, perverting. Adversity, in many 
instances, but not in all, improves the disposition. 

LOGIC OF CHARACTER. 

21. The Science of Character has reference to the 
proportionate development of the sensibilities and powers 
in different Individuals. It presupposes the Science of 
Mind. 

Human beings in general have certain susceptibilities to 
Feeling, powers of Volition, and aptitudes of Thought ; all 
which possess degree, and may be unequally manifested in 
different persons. Hence, an individual mind is not suffi- 
ciently described by its participation of our universal mental 
nature ; but must be represented according to the proportion- 
ate development of the several Feelings, &c, common to 



BASIS OF THE SCIENCE OF CIlAKAri ;, | ; 

humanity. We are all liable to Fear; wo all p 
Affection ; but some more, some h 

It is impossible to state these peculiarities of c 
except in the language applicable to mind universally; 
analyze a character without having first analyzed the mini 

The basis of any Science of Character most, then 
the ultimate analysis of the Mind. There should be B 
tained, as far as possible, the native ami irresolvable I 
and the attributes of Volition and of Thought. 1 
were like a mineral, the statement of the degrees of I 
various fundamental attributes would be the account 
character. But the mind is a thing of indefinite growth, 
adaptation, acquisition; its first cast is greatly altered before 
the end ; and, as what we usually desiderate is the char; 
of a full-grown man or woman, we must provide an account 
of the acquired, as well as of the native powers. 

The proper view to take of Phrenology is to regard it as a 
science of Character, accompanied with a theory of external 
indications. It furnishes a professedly ultimate Analysi 
the Mind. It farther endeavours to connect each mental 
power or susceptibility with a local habitation in the brain, 
outwardly manifested by the shape of the head. This addi- 
tion, although highly convenient, is not necessary to constitute 
a science of character. 

22. In the description of characters, there is obviously 
wanted a scale of degree. 

The difficulties attending the quantitative estimate of mind 
are a serious drawback in the science of character. Yet it is 
impossible not to make the attempt to distinguish more and 
less in the various mental attributes. 

The ordinary mode of procedure is this. In each Bepai 
peculiarity — emotional, volitional and intellectual — we form 
an estimate of the general average of persons known t<> us. 
Above and below this average, we use the indefinite adjectives 
of quantity, — much, great, very great, small, very small, defi- 
cient, and so on. 

The scale of Phrenology includes a wide range of degl 
probably beyond what can be practically discriminate.; 
agreed upon. 

Our most correct appreciations of quantity in mind, 
upon an objective basis. Thus, a slow learner can be 
pared with a moderate or a quick learner, through the lei 






518 LOGIC OF CHARACTER. 

of time required by each for a given amount of acqui- 
sition. This objective method admits of a considerable 
amount of precision, and is the chief hope of attaining 
quantitative accuracy in the Science of Mind. 

23. The native Elements of Character would be con- 
veniently represented under the three heads — Activity, 
Teeling (Emotional), Intellect. 

The detailed account of these elements is the adaptation of 
'he psychological analysis of the mind, to the statement of the 
basis of character. 

The mental elements might be prefaced by an account of 
the important physical organs implicated in mental processes, 
so far as regards their physical characteristics. The Brain, 
the Muscular S3 T stem, the Digestive System, &c, of each 
individual, might be regarded, in the first instance, from the 
objective side, or as viewed by the physiologist and physician. 
These organs have all bearings, direct, or indirect, on character. 

In recounting the native elements of Activity, Feeling, and 
Thought, we need to single out for special consideration the 
Intellectual Hetentiveness, as being the expression of the 
possibilities of growth, acquisition, or education. This is the 
foremost law of mind, with reference to the moulding or 
Formation of Character, the means of transforming the various 
native tendencies into an artificial cast. The educability of a 
character needs to be looked at by itself ; a thing only to be 
determined by actual experiment of the progress in given cir- 
cumstances. The schoolmaster, after a certain length of pro- 
bation, judges whether a pupil will succeed in Mathematics, in 
Language, or in Drawing. 

24. In estimating Character, whether in fact or in 
expectation, we must never drop out of sight the Law of 
Conservation, under the guise of the Limitation of the 
Powers. 

The accurate judgment of an individual either as exhibited 
at any one time, or as regards the possibilities of transforma- 
tion, must depend upon the precision of our allowance for the 
Limitation of the Powers. Dealing with persons averagely 
constituted, we cannot expect a development above average 
in one region without a falling off in some other ; and so on, 
through all varieties of assumption as to the extent of the 
powers on the whole, and as to the proportions of each. 



INFLUENCES ON CHARACTER. 

25. The subordinate laws of Character are I 
of the operation of Circumstances on I mation of 

iracter. These must be handled in detail, under th 
fluent lights of actual experience and of the supei 

The circumstances that influence character are and 

inexhaustible. They afford a wide exemplification of Induc- 
tion coupled with Deduction— Empirical | 
into Derivative. They also exemplify the prevailing laxity in 

(the use of the method of Agreement. 
The leading circumstances are such as these : — 

I. The physique of the individual, viewed from its purely 
physical side; the comparative strength or weakness of the 
different physical organs. A whole series of consequences 
to the character follow from the purely physical endowments. 
Great muscular strength gives a certain direction to the activi- 
ties and pursuits, whatever be the proper mental tendencies. 

II. The physical treatment of the system, in all that regards 
nourishment and the adjuncts of health. The consequences 
of these are the greater or less total of force, to be distributed 
among the various functions, including the supports of mind. 
Climate, town or country life, poverty or affluence, indulgence 
or temperance, are obvious elements of this computation. 

III. Natural surroundings, as they affect the mind — the 
activities, feelings, or intelligence. Differences have often been 
pointed out as between mountaineers and tenants of the plains, 
between sea-faring nations and those in the interior of conti- 
nents, between rural and urban populations. Not much 
precision has as yet been gained in the expression of those 
differences. But, if studied by the double method of induction 
and deduction, they may yield important laws. 

It is a clear deductive truth that variety of impressions must 
enlarge the compass of the intellect. It is not so obvious what 
will be the effects on the feelings; the aesthetic sensibilities, 
for example, are not quickeued by nature alone ; they usually 
need another stimulus. Incessant familiarity with seem 
grandeur has less effect (on the Law of Relativity) than alter- 
nation of these with others of a tamer sort. 

IV. Modes of Industry, or habitual occupation, erivo a 
notorious bent to the character. The effects of occupation or 
profession have been a subject of frequent observation ; many 
of the consequences being apparent. The soldier, the sailor, 
the tiller of the ground, the trader, the priest, have each the 
Btamp of their calling. 
23 



520 LOGIC OF CHAKACTER. 

V. The Surrounding Society moulds the individual as to I 
feelings, and as to modes of thinking, in ways too numerous 
to exhaust, but yet capable of being stated with remarkable 
precision. The inductive empiricisms on the one hand, and 
the deductive principles, on the other, conspire to express the 
remarkable assimilation of the individual to the society; 
while it is not difficult to point out its limitations, the circum- 
stances being given. The religious, ethical, and political 
opinions of each person are, in the great mass of cases, the 
exact reflex of what prevails in the society about him. 

VI. The express Education given by the schoolmaster 
should be added to the moulding influence of general society. I 
This element admits of being clearly stated. A people 
sent regularly to school like the Scotch, or the Germans, I 
acquires a distinct superiority of intellectual and moral 
character. Under this head, attention must be paid to the 
educational influence of Institutions ; as, for example, an 
established church. 

VII. The amount of Liberty permitted to individuals by 
the state, and by society, has a vast influence on character, r 
The revolutions that have achieved enlargements of individual I 
freedom, as the Protestant Reformation, are experiments of I 
Difference, showing the impetus given to progress by Liberty. I 

Political freedom is not exactly the same thing as Self- * 
government, but is not complete without that addition. This 
too i3 an instrumentality for moulding the character. 

VIII. Many Social Institutions, Laws and Customs, apart 
from the general fact of Freedom with Self-government, 
exercise on character an influence that may be studied and 
assigned. The tenure and descent of Property, the Marriage 
Laws, improved means of Communication, are obvious in- 
stances. 

From the foregoing remarks, will sufficiently appear the 
Notions, the Propositions, and the logical Methods of the 
science of Character. It will be advisable, farther, to note 
the heads of Classification ; which will serve as an important 
preparation for the Logic of Politics. 

Classification of Characters. 

26. The classification of Characters is not a proper 
classification according to the Natural History mode. 

We could not, except by a useless fiction, arrange charao 
fcers in Orders, Gen >ra and Species. The real distinction be- 



PECULIAMTIKS OF C1IAK.UTI.K. 

tween characters is expressed by the higher or low 

of some one or more of the ultimate elements of c 
And we do not find characters agreeing in a plu 
common attributes, excepting so far as the elevation oi 
peculiarity implies the depression of some others ; and b 
we have no basis of generic or specific agreements. The only 

ible way of giving an exhaustive acconnt of char 
to assume by turns a higher degree of each peculiaril 
Active, Emotional, Intellectual, and to state the appeal,. 
connected with that; whence by obverse inference w 
gather the concomitants of the low degree in each 
Thus, we could indicate the general consequences of an nnn 
pitch of Natural or Spontaneous Energy; of the Emotional 
Temperament on the whole, and of any of the special si; 
tibilities to Feeling or Emotion, as Organic Sensibility, Sight, 
Tender Emotion. 

There is no limit to the possible modes and varieties of 
character arising out of the conjunctions of different facn 
in excess or in defect. These conjunctions, however, mnst be 
governed by the laws of their elements; so that their explana- 
tion is purely deductive, under the check of actual ca 

27. The details of Character are thus the account of the 
separate peculiarities, followed by the analysis and expla- 
nation of such select conjunctions as are often found, and 
are of practical importance. 

Under the head of Action, we have important varieties — as- 
indolence, general or partial, fitfulness of energy, and steady 
persistence. The Emotional character is yet more varied ; 
under it we have the dispositions expressed by sensnal, sensu- 
ous, sociable, reverential, irascible, egotistical, and bo on. 
The aspects of Intellect are more numerous still ; general 
ability, general stupidity, aptitude for language, for science, 
tor art, for business, and many other still more special m 
The attributes involved under Conscience are a very m 
product. That predominance of the Love of Gain — man if 
from ancient times by the Jews, and in modern timea by the 
English, and the peoples sprung from them — >nght to bo 
traceable to constitutional foundations coupled with circum- 
stances. The sense of Dignity, united with respect for the 
Forms of Law, and the regard to the Practical and Concrete — 
as combined in the ancient Roman— oiler an interesting subject 
for analysis and explanation* 



522 LOGIC OF MINERALOGY. 

The distinctive characters of the Sexes are to be soughi 
by the same analytic procedure. These refer us to pbysica 
foundations, as well as to mental elements and to the opera- 
tion of circumstances. 

The problems of character take a practical shape in Educa- 
tion ; being an enquiry into the means of moulding charactei 
according to prescribed types — Active, Emotional, Intellectual 
The experience of the educator is the verification of the 
deduced maxims. 

Under the Logic of Politics, there will be a further occasior 
for applying the science of character. 



CHAPTER VI. 
SCIENCES OF CLASSIFICATION. 

Mineralogy. 

1. Mineralogy is a Concrete, Descriptive, Classificatorj 
science, referring to the solid inorganic constituents of the 
globe. 

A Mineral is defined as a solid homogeneous body 
having a definite chemical composition and a definite 
crystalline form. 

Mineralogy brings forward no new laws or operations. It 
merely applies mathematical, physical, and chemical laws tc 
the inorganic solid constituents of the globe. Moreover, it i* 
not so^ much engaged in tracing physical sequences as in 
arranging and classifying the multitudinous materials we find 
in the earth's crust. Its laws are laws of co-existence, as 
Co-inherence of Attribute. 

The science of Mineralogy is in close connexion with 
Chemistry. Had Chemistry attained its present advanced 
shape at an earlier period, there might have been no separate 
science of minerals. Bat for the comprehensive treatment oi 
all material elements whatsoever, under Chemistry, there 
might be an objection to the exclusiveness of Mineralogy, in 
refusing to take account of liquid and gaseous bodies, as 
water and air. Yet, seeing that all these are sufficiently given 
m Chemistry, there is no need for repeating them in another 



I 






MINERALS DEFINED. 



science ; and Mineralogy retains its special ami n 
scope, which is to treat of substances presenting forn 
as definite composition. 

The chief advantage of detaching Mineralogy from I 
try is to enable minerals to be more fully described in their 
minute varieties, and to be more comprehensively classiti «1. 
The separation relieves Chemistry of a burden, and alio 
fresh start in the process of classifying. 

Definition of a Mineral. — Into the definition of a mineral, 
two main facts enter, and these dictate the whole plan of the 
science: — Chemical Composition and Crystalline Form. Aj 
regards the first point, minerals are either simple bodies or 
chemical compounds; and as chemical compounds, they mast 
be homogeneous substances, and not conglomerations of 
different material like a piece of pudding stone or of granite ; 
such conglomerates are not minerals but rods ; quartz is a 
mineral, gneiss is a rock. 

As regards the second part of the definition, minerals have 
a definite Form; a fact associated with their homogen 
character. The simple substances in their purity, and the 
definite chemical compounds, when in their highest degri 
.consolidation, assume definite crystalline shapes; and the 
occurrence of these shapes is a further guarantee of the bom >- 
^eneous nature of the material, allowance being made for 
the property called isomorphism, or the existence of similar 
forms in different materials, which permits of their crystallizing 
together. 

The definition excludes clay, sand, and soils, these bung for 
ihe most part heterogeneous, as well as formless. 

The deposits from organic bodies, as coal, amber, and 
mineral resins, are improper minerals ; they have neither 
purity nor form. 

I. Arrangement of Mineral Characters. 

2. The exhaustive statement of Characters, in Mill 
logy, is substantially the same as in Chemistry. 

Under the Logic of Chemistry, we discussed the gni 
principle of arrangement of characters, namely, to tollow the 
expository order of the properties: from which was deduced 
the following sequence. 

I. Crystalline Form. n_ g 

II. Optical properties, including Refraction, Double &>&•*■ 
tion and Polarization ; Colour ; Lustre 



521 LOGIC OF MINERALOGY. 

ITI. Specific Gravity. 

IV. Cohesive properties, namely, Hardness, Tenacity, Elas- 
ticity. To these three heads are reducible Brittleness, Duc- 
tility, Malleability. 

V. Adhesion. This means the cohesive nnion of different 
substances, without chemical affinity; the leading cases are 
solutions, alloys, and cements. It might be the head for 
entering the composition of those bodies that are treated as 
alloys and not as chemical compounds. The isomorphous 
unions are of this nature. 

VI. Relations to Heat. Rate of Dilatation by increased 
temperature ; Melting and Boiling points ; Conduction of 
Heat ; Specific Heat ; Radiation, Absorption, Refraction, and 
Polarization of Heat. This is the exhaustive array of proper- 
ties having reference to heat ; and probably includes more 
than the mineralogist is ever accustomed to state, they being 
unknown for the greater number of minerals. 

VII. Relations to Electricity : — Magnetic property ; Con- 
duction or Isolation of Electricity (Frictional and Voltaic); 
place in the Electric series, from Electro-positive to Electro- : 
negative ; place in the Thermo-Electric series. 

VIII. Chemical properties. The mineralogist is not sup- j 
posed to transcribe the whole chemistry of each substance. I 
For his purposes a selection is made of chemical re-actions I 
useful in mineral testing. 

Occasionally minerals have Taste and Odour. 

How far any of these properties can be related, by general 
laws of Causation or of Co-existence, with any other proper- 
ties, is an important enquiry falling under Molecular Physics, i 
and is not especially the business of the mineralogiat. Such 
laws of connexion as may be established, simplify the study of \ 
minerals, by making one property the index of another. That 
there are such laws is certain ; several have been noticed in 
former connexions (Book III., Chap. III. § 3). These laws, 
however, do not, as yet, dispense with the separate statement 
of the properties above given, although they may give to 
several of them a derivative character.^ 

The fact of there being laws of connexion of the properties 
his an important bearing on the next head. 

II. The Maximum of Affinity of Minerals, as guiding their 
Classification. 
3. It has to be seen what classification of minerals best 
complies with the golden rule. 




BASIS OF MINERAL CLASSIFICATION. 

'o bring together things that have In common 
number of leading attributes, is the first condition o! 
Bcation. Now we have above enumerated eight difl 
groups of mineral characters ; and the question arises, * 
of all these should be the groundwork of the arra into 

classes. 

There are two suppositions that, if true, would facilitate 
the decision. First, if by the discovery of laws of mutual 
connexion, any one of the groups of properties v 
one or two other groups, there would bo a redaction ol 
total number of alternatives. Thus, if Crystallization \ 
related to the modes of Cohesion, or if Electrieal and Chemical 
properties were found to be allied, we should be able to assume 
one of the allied members as representing both. 

Again, if any one group of properties, by intrinsic import- 
ance, and apart from the association with another group, had 
an obvious and marked predominance, such group would ho 
properly chosen to give the lead in the classification. In this 
point of view, for example, the Crystalline arrangement might 
be fairly preferred to either Heat or Electricity. 

On both, grounds, preference is to be given to these two 
characters; namely, Chemical Composition and Crystalline 
Form. Accordingly, these are employed as the groundwork 
of classification. Minerals are first divided according to their 
Chemical Composition; and farther subdivided according to 
their Crystallization. In the mineral collection of the British 
Museum, arranged by Mr. Maskelyne, no other property is 
employed as a basis of division. 

In the older classifications, other characters were mad 
of. The system of Mohs proceeded on Crystalline fnrm, Hard* 
ness, and Specific Gravity. Now, Hardness, which we may 
otherwise express as cohesive energy, must be a result of the 
molecular forces and arrangements accompanying chemical 
constitution and crystallization, and, from this eircumst 
alone, is peculiarly unsuited to be a primary foundation of 
classes. Again, Specific Gravity may likewise he viewed 
result of the molecular arrangements, under which the ulti- 
mate particles attain to greater or less proximity. 

The arrangement of Weiss is in its chief basis chemical ; his 
primary division into Orders is governed by chemical compo- 
sition purely: — Oxidized Stones, Saline Stones, Saline I 
Oxidized Ores, Native Metals, Sulphuretted Metals, Inflam- 
mables, In subdividing the Orders into Families, he brings 
into play other considerations. Thus, importance in the com- 



520 LOGIC OF MINERALOGY. 

position of rocks, or in the geological stratification of the globe, 
determines such families as Quartz, Felspar, Mica, Hornblende, 
Garnet. Again, the precious stones, or gems, notwithstanding 
diversity of chemical composition, have a remarkable agree- 
ment in such characters as hardness, tenacity, high specific 
gravity without metallic aspect, transparency, vivid colours. 
We may, however, fairly doubt whether either of those two cir- 
cumstances is enough to justify mineralogists in departing from 
the arrangement according to the great primary attributes — 
Composition and Form. In such cases, a supplemental arrange- 
ment should be made for the specific object in view, without 
distorting the one principal scheme. The geologist, to prepare 
for describing the stratification of the earth's crust, may select, 
and array for his own purpose, the predominating mineral 
constituents. And, with a view to the popular interests of the 
subject, the mineralogist may bring together into one group 
all the substances that combine the most highly fascinating 
properties of external appearance. 

The arrangement in the British Museum can be briefly re- 
ferred to, as carrying out the scheme according to Composition 
and Form. 

The first division is into Native Elements, or Simple Bodies, 
and Compounds. 

In arranging the Native Elements, there is an inversion of 
the usual order in Chemistry ; the Metals precede the Non- 
metals. This is owing to the predominance of the fact of 
Solidity in the mineralogical view of the earth's constituents. 
The native metals, therefore, come first of all ; and in deciding 
their arrangement among themselves, no farther chemical 
circumstance is taken into account ; the reference is solely to 
Crystallization. 

Under the first System of Crystallography, the Cubic, are 
arranged, Copper, Silver, and Gold. Under the fourth System, 
the Hexagonal or Rhombohedral, are the isomorphous metals, 
Arsenic, Antimony, and Bismuth ; and the same forms brings 
into continuity with these the rare metal, Tellurium. 

The Non-metallic native elements are Carbon and Sulphur ; 
Carbon being found in the two mineral forms— Diamond and 
Graphite. 

Compound Minerals. — The native metals occur often as 
alloys ; and these are included with the simple minerals ; an 
alloy is not a chemical compound. The chemical combination 
of the metals takes place chiefly with the non-metals ; the 
prominent instances of combination with other metals, are the 



MINERAL COMPOUNDS. 

compounds with the Arsenides— Arsenic, Antira mth. 

► Accordingly, the Arsenides, &c, are the commencing dii 
of compound minerals; the subdivisions, as in tbo n 
elements, being according to form. Tin 
Tellurium, Selenium, and Sulphur, are chemically grouped 

bher, under the name * thionid' elements, and their i 
pounds with the metals — Tellurides, Selenides, Sulphi ; 
are next in order ; there being subordinate arrange units 
according to the crystalline systems, which are nearlj 
represented. There are also divisions according to .-till higheff 
compounds, as when Arsenides, &c, unite will; Salphii ; 
which higher compounds succeed in order to the simple com- 
pounds. 

The next division comprises compounds of the Metals with 
the non-metallic group — Chlorine, Iodine, Bromine, Fluorine — 
the ' halogens.' Under these fall certain conspicuous substan- 
ces — Common Salt, Calomel, Sal ammoniac, Fluor Spar, 

The remaining first rank Division of compound minerals la 
the Corrqiounds of Oxygen — a division of enormous extent, and 
progressive complication. The chief subdivisions are there- 
fore chemical, the distinctions of crystalline form being reserved 
for the final subdivisions. Commencing with bodies having 
the lowest equivalents of oxygen — the Monoxides, we are led 
to the higher equivalents — the Sesquioxides and Binoxides ; 
under each of these heads, the farther subdivision is according 
to crystalline systems. Next are the Oxygen Salts, of which 
the Carbonates are an extensive group of minerals, divided by 
their crystalline forms into Prismatic, Rhombohedral, and 
Oblique. After these come the Silicates, a large, varied, and 
important class of minerals, subdivided chemically in the first 
instance, and by crystalline form in the end. To these sue 
Borates and Nitrates. The final groups are Phosphates and 
Arseniates, which, in consequence of the isomorphisms of cor- 
responding compounds of Phosphorus and of Arsenic, cannot 
be classified apart. 

If it be the fact that the two properties— Chemical Compo- 
sition and Crystalline Form— have a commanding prominence 
in minerals overshadowing the others, or else carrying these 
along with them, the foregoing classification is in the hi 
degree natural or philosophical, being accordant with the rule 
of the maximum of resemblance. 

4. The Chemical Composition and the Crystalline form 
also give the proper boundaries of Species. 



LOGIC OF MINERALOGY. 

The question as to the boundaries of species presents nc 
etical difficulties on the above scheme. Every native 
clement, nnd every definite chemical compound, would consti- 
tute a well-marked species, an Infima Species, or lowest kind. 
If the same element, or the same compound, has two allotropic 
forms, as Carbon, these are distinct mineral varieties, but 
would not be proper species. 

The practical difficulties attending mineral species arise 
from combinations not chemical, where the elements may be 
in all proportions; as in the isomorphous compounds, thei 
alloys, and .the admixture of foreign ingredients generally. 
Such instances are proper varieties, and receive distinctive 
names and separate descriptions whenever tbe difference is of 
a marked kind. 

III. Classification by Grades. 

5. The Grades in Mineral Classification are used merely 
for arrangment, and not for shortening the description of 
Mineral Species. 

In the scheme of TVeiss, there are three grades — Orders, 
Families, and Species; an irrelevant and illusive semblance of I 
the classification in Botany and in Zoology, where the ' 
several gradations — the Orders, Families, &c— are each ac- 
companied with a definition, or enumeration of common 
characters. A Mineral Order, on the other hand — as Oxidized 
Stones, Native Metals— is accompanied w T ith no definition, and 
suggests no common characters beyond what is gathered from 
the name. So with the Families. The family ' Quartz ' in 
the order ' Oxidized Stones ' is not defined as a family ; there 
are no characters assigned as common to all the species of 
the quartz family. There is a title OXIDIZED STONES, a 
sub-title Quartz; and then commences the enumeration of 
species ; so that each specific description contains all the 
characters of that species, exactly as if it stood alone in the 
world. The Gradation, therefore, is a Division, but not a 
Classification. 

In the scheme of the British Museum, the division begins 
with the dichotomy of Native Minerals and Compounds. The 
Native Minerals are not again divided formally; they are 
simply arranged in the order of crystalline systems. The 
Compounds involve various subdivisions, which could easily 
be laid out in the tabular form. As there is no systematic 
treatise on Mineralogy based on the scheme, we do not know 



UNIFORMITY IN STATEMENT OF CfiARA I 

whether the gradation could be properly converted into i 
system of Orders and Families, in the proper 
enumeration of the characters of those orders and fam 

but, in all likelihood, no such attempt would be mi 
Chemistry nor Mineralogy can gain much by straining 
parallel of Botany and Zoology in this respect. 

IV. Marking of Agreement and Dif 

6. The exhibition of Agreement and Difference in Min 

description is gained in the following ways. 

(1) By observing a uniform plan. 

(2) By proximity of species according to the maximum 

of agreement. 

(3) By select comparisons. 

(4) By select contrasts. 

From the absence of defining characters m the higher divi- 
sions (except as indicated by the significance of the names) 
the best means of stating agreements is wanting. If the nature 
of the case does not permit of the operation of giving characters 
to Orders and Families, we must proceed by other ways. 

(1.) A uniform plan in the statement of the characters gives 
a facility of comparing any one species with any other. This 
is carried out in works on Mineralogy, although not with all 
the aids that typography might afford. 

(2.) It necessarily follows from a good classification that the 
species placed in close proximity have the' most numerous 
points of agreement, or the fewest points of difference. When 
native metals are arranged in crystalline forms, the contiguous 
species have a very large amount of similarity, and compara- 
tively few dissimilarities. This produces on the reader the 
effect of a classification by grades, with agreements stated at 
each grade. 

(3) The mind receives great assistance from separate tables 
of agreements, on select properties. Thus, it is conveniei 
tabulate the minerals falling under distinct crystalline foi 
those having the same specific gravity; the same hardi 
&c. This is a great supplemental aid to the mental corn pa r 

of individuals. 

(4) Select contrasts. When important minerals are nearly 
allied, and apt to be confounded, they should be brought 
direct comparison, through a statement of the agre< 

nres, and a tabular contrast of the differences. For example, 
Platinum and Palladium have a very close resemblance, 



530 LOGIC OF MINERALOGY. 

mi slit have their agreeing characters given together, and their 
differences formally contrasted. 

V. Index Classifications of Minerals. 

7. For the ready determining of Minerals, recourse may 
be had to Index Tables. 

The properties apparently most suitable are — Crystal- 
lization ; Transparency, Lustre and Colour ; Specific 
Gravity; Hardness ; Chemical and Blow-pipe re-actions. 

Of the two chief modes of constructing an Index — a succes- 
sion of Dichotomies, and Tabulations — the first is exemplified 
in Botany, the second seems adapted to the present state of 
Mineralogy. The thing requisite is to tabulate all known 
minerals according to every one of these properties, so that 
when any one property is ascertained, a reference to the table 
for that property will show what group it belongs to, and 
thereby limit the search. The discovery of a second property, 
in like manner, gives a reference to a second table, and 
reduces the choice still farther. 

The first table — Crystalline Forms — would be arranged in 
the order of the crystalline systems, and the important 
varieties of each, and would also be adapted as far as possible 
to the indications of the goniometer, which measures the 
angles. 

The Optical properties, Transparency, Translucency, Lustre, 
Colour, might demand several tabulations — one for modes of 
Transparency and Translucency, another for Lustres, a third 
for Colours. There are doubts, however, as to the practical 
utility, for purposes of discrimination, of the table of colours; 
since, although colour is an important mark in pure substances, 
the admixture of colouring matters is so frequent as to render 
the test misleading. 

A Table of Specific Gravities would be useful as a means of 
testing. Many substances are well marked by specific gravity. 
The different varieties of the important group of Dolomites, 
or magnesian lime stone, are most conveniently distinguished 
by this test. 

Hardness being reduced to a scale of degrees, and being 
easily tested, is a valuable aid to discrimination ; for which 
end there should be a table of minerals according to degrees 
of Hardness. 

With a view to Blow-pipe and Chemical testing, there are 
needed corresponding tables for each characteristic appear- 



CHARACTERS FROM PAHTS OK PLANTS. 

ftnce; as fusibility or in fusibility, solubility m , 
This is merely a modification of the met 
Chemistry. 

Each of the Index tables might contain columns for the 
other important index properties, so as to give all bii 
ters at a glance. 

These tables farther point out Agreements among mine 
and furnish one of the modes given" for that purpose under tho 
preceding head. Their use in suggesting Laws of Co-existenoe 
or of Causation, among the properties of bodies, ia sufficient 
to give them a place among the Arts of Discovery. 

BOTANY. 

I. Arrangement of riant Characters. 

8. The arrangement of the characters of Plants follows 
the expository order of the parts of the Plant, 

This is the principle already exemplified in Mineralogy, and 
applicable to all sciences of classification. 

In a complete system of Botany, the First Division — Struc- 
tural and Morphological Botany — enumerates the pari 
Plants as a whole ; giving a generalized and methodical 
account of all the structures found in all known plants. 

Commencing with the constituent Tissues of Plants, this 
division includes — Cells and Cellular Tissue ; Vessels and 
Vascular Tissue ; the Contents of the Vegetable Tissues — 
starch, gum, sugar, oils, resins, &c. ; the Integumentary 
Tissues — as hairs, glands, and other appendage 

Plants differ in the modes of these constituent 
Thus, the Acoiyledons are cellular plants without vessels, or else 
vascular plants with scalariform vessels ; the Monocotyl 
and Dicotyledons are vascular plants with spiral vessels 
storaata. 

The Organs or parts of Plants are divided into Nutritive 
and Reproductive. The nutritive are the Root, Stem, 
Leaves ; the reproductive, the Flowers, and Fruit. An enume- 
ration is given of all the different forms assumed by ea 
throughout the entire assemblage of vegetable species, 'i 
might be, under each separate peculiarity, a tolerably ex! 
tive reference to the plants possessing it. By BUcb mean 
information respecting species is repeated in a different i 

To this department of general Botany succeeds V 
Physiology, which, however, has only an indirect b 
the Classification of plants. Any peculiarity of function in an 



532 LOGIC OF BOTANY. 

individual species would be stated tinder the organ concerned. 
Thus some cellular plants, as Oscillatorias, bave undulating i 
movements in the cells ; and some, as Confervas and Diato- 
viacea*, conjugate, that is, unite their cells in reproduction, | 
by means of an interposed tube. 

The next great division, called Taxological Botany, embraces 
the Classification of Plants, with the Description of each. 
The principles of Classification will be considered nnder the 
subsequent heads. The order of Description is the order of 
the parts in Structural Botany, as above quoted : — Cellular 1 1 
Tissue, Vascular Tissue, Contents of Cells ; Boot, Stem, 
Leaves, Flower, Fruit. 

In referring to a work of Botany for the description of any 
given plant, we shall not find, as in Mineralogical treatises, 
a consecutive and exhaustive account of characters. Two cir- 
cumstances stand in the way of such a description. 

In the first place, the system of grades, which is inoperative 
in Mineralogy, is thoroughly worked in Botany. Hence to 
exhaust the characters of a species, we must ascend through 
all the grades, collecting the characters of each, and nnitiug 
them in one series. The characters of the ' Common Haw- >j 
thorn 1 are distributed (1) nnder the species so named, (2) under I 
the genus i Hawthorn ' (Crataegus), (3) under the family 
'Rose' Rosacea), (4) under the class, 'Dicotyledon.' By 
assembling the common characters of the class, the family, 
the genus, and the species, in the proper order, we should 
have a full description of the Hawthorn. 

In the second place, most works on Botany do not profess 
to exhaust the known character of species, or to give under 
each species the whole of the information that exists respect- 
ing it ; so that even after collecting the characters from all 
the gradations, we bave not the full knowledge of the species. 
The reason is, partly, that botanical treatises are usually con- 
fined to the humbler function of determining or identifying 
plants; partly, that the full information, while very volumi- 
nous, is seldom asked for ; and partly, it is to be feared, from 
vacillating between the two ends — determination and informa- 
tion. 

II. 1 he Maximum of Affinity of Plants as guiding their 
Classification. 
9. In considering the characters of plants, with a view 
to classification, we find the order of description to be also 
the order of relative importance. 



CONCOMITANCE OF TISSUES AND 

The circumstance that most of all gives importance t» a 
character is the number of other characters I 
with it. Supposing all the characters of eqnai intrinsic 

value, any one that represents three others is lour times the 
value of one that represents only itself. 

There is a correspondenee or concomitance of characters in 
the fundamental parts of plants — Elementary T Nutri- 

tive Organs, and Reproductive Organs — which facilitates 
natural groupings. When we assume as a bas 
this class of characters, we secure at once a large amount of 
Agreement. Isolated characters, as Colour and Odour, give no 
help to classification. 

Now it is found that the Elementary Tissues are the most 
important in this view ; next are the Nutritive Organs ; and 
lastly, the Reproductive Organs. Certain forms of the Ele- 
mentary Tissues are accompanied with definite modes in the 
Organs, both nutritive and reproductive. By the Tissues 
alone, Plants are divided, in the first instance, into Cellular 
and Vascular; the Cellular comprising the lower trib 
Lichens, Seaweeds, and mushrooms; the Vascular, the higher 
fiowerless plants and the flowering plants. Thus, the dis- 
tinction marks the lower and higher in organization. 

In the Nutritive organs, the embryo is the part of greatest 
importance ; on it rests the grand ternary division into Ac>ty- 
ledons, Monocotyledons, and Dicotyledons, which repres 
numerous and important differences, and is, therefore, in the 
highest degree a natural or scientific division. Second in 
importance to the embryo, or seed, is the root, on which is 
based a triple division — Heterorhizal, Endorhizal, and i 
rhizal. After the root comes the stem, by which is marked the 
great division into Exogenous and Endogenous, together 
with the farther division into Acrogenous and Thallogenons. 

In the Reproductive System, the stamens and the pistils 
occupy the first place ; these were the chief basis of the Linneao 
Artificial or Index system. They are the essential o 
the Phanerogamia, or flowering plants ; and have an ana! 
in Cryptogamia, or fiowerless plants. Next to those in \ 
is the fruit; and after it, the floral envelopes; and finally, in 
flowering plants, are found the inflorescence and hm 

Thus, b}^ classing according to the characters that carry vt 
them the greatest number of other characters, there is gained 
the maximum of affinity on the whole. On the great lea 
divisions this is effectually secured. The difficulties ari 
disposing of the families or Natural Orders, of which a large 



; 



534 LOGIC OF BOTANY. 

number is included in the immediately superior classes (or 
sub-classes) ; GO Natural Orders are contained in the first sub- 
class of the Dicotyledons (Thalamiflora?). It is impossible to 
arrange these upon any one principle of succession or contig- 
uity ; whence such devices as circular arrangement, double 
placing, &c. After describing any one Natural Order, Lindley 
exhibits it diagramatically in the centre of four other orders 

right, left, above, beneath — so as to show its alliances on 

different sides. 

A still greater difficulty is presented by the transition 
classes, which, with reference to the others, are denominated 
aberrant, as departing from a recognized assemblage of 
characters. At the end of the enumeration of a class is some- 
times given detached an anomalous or aberrant member, 
which, however, by the very fact of its isolation, is a new 
class. The genus Spleenwort (in tbe Fern family) is a re- 
markably well-characterized and natural genus; yet a few 
species are scarcely to be distinguished from some species of 
Shieldfern and Polypody, except by the sori. 

III. Classification "by Grades. 

10. Botany is the happiest example of Classification by 
Grades. 

It is a peculiar circumstance in Botanical classification, that 
the higher divisions are made upon the more fundamental 
characters (the Tissues) ; that the next sub-divisions are upon 
characters next in order of importance (the Hoots, &c.) The 
Natural Orders or Families are characterized by general 
structure, but especially the Flowers and the Fruit, The 
characters of the Genus are a continuation of those in the 
Order. In the Species, the differential marks embrace Stem, 
Leaf, and Flowers. The tendency of this arrangement is 
to reduce to comparative insignificance the distinctions of 
Species. 

For practical purposes, great interest attaches to the various 
products or deposits in plants — starch, sugar, gum, oil, resins, 
&c. These special products often prevail through Natural 
Orders, while sometimes they attach to Genera, and sometimes 
to Species. 

The motives for settling the lowest Species, as distinguished 
from Varieties, were formerly stated. Constancy or perma- 
nence of characters is one of the conditions. Tnus the Water 
Ranunculus assumes many striking variations of form, which 



SPECIES OF TLANTS. 

have been regarded as specific distinctions; but fn 
inconstancy, and their dependence upon sitnati 
more correctly deemed Varieties. St., Colour i 
that must be generally withheld from specific 
given as a variety. 

A plurality of important characters is the best work 
of a species. The sweet orange and the bitter oranj 
garded as Varieties ; the lemon is held to be a distincl 
the points of difference between the sweet and bitti r 
are fewer than the differences between the orange and the 
lemon. 

In the inferior forms of Plants, the specific murks are i 
very limited in. number, although they may refer to or 
high in the scale. Thus, in the Ferns, the limitation of both 
genera and species has always been a matter of difficulty. The 
chief reference is the fructification, or the arrangement of the 
seed; a character of high fixity and permanence in plants 
throughout. In grasses too, the limits of the numerous l: 1 
are not clearly fixed, — a proof of the fewness of available 
characters. 

The apparatus of Grades necessarily collapses when the 
organization is not of a sufficiently high order to allow of a 
series of halting places with important community of attri- 
butes. The eight, ten, or twelve steps of descent that may be 
interpolated in the more elaborately organized BicutijhuJ'juous 
Orders, are reduced to three or four in the Grasses and Ferns ; 
while it may be difficult to maintain even that number in the 
Fungi, Lichens, and Sea-weeds. 

IV. Marking of Agreement and Difference. 

11. The system of Grades so far provides for the state- 
ment of Agreements. 

We have frequently called attention to Agreement and 
Difference as the fundamental facts of all knowledge. The 
more thorough the provision for exhibiting these two f 
the better will the subject matter be known and undersf 

By forming a class, we indicate a community of attribi 
and everything should be done to exhibit the Agreement 
plainly. The tabular form is more particularly Baited to 
characters that can be expressed shortly. It is a grand 
mistake to suppose that the forms and typography of ordinary 
composition are suited to the generic and specific description* 
of plants or of minerals. The different heads of tho descrip- 



536 LOGIC OF BOTANY. 

tion are seized with difficulty when scattered indiscriminately 
over the printed lines — sometimes at the beginning, and some- 
times at the middle or at the end. Any remark on a character, 
by way of commentary, or explanation, involving the composi- 
tion of one or more sentences, should be printed in the compact 
form of ordinary composition : but the broken, unsentenced 
description of characters should be exclusively tabular. Such 
expressions have already the reality of a table, and to deprive 
them of the form, in order to make them seem composition, is 
to withhold the only advantageous mode of presenting them 
to the mind. Thus to take the genus Ranunculus described as 
below* : — 

The first sentence, containing a very general remark, may 
stand as it is, out of the tabular form : * Annual or perennial 
herbs, sometimes entirely aquatic \ this should be coupled 
with the sentence that comes after the description, as to the 
geographical spread of the genus. The proper descriptive 
characters are strictly matter for a table, thus : — 

Leaves, entire, or more or less divided. 

Flowers, usually yellow or white. 

Sepals, 5, very rarely reduced to three. 

Petals, 5 or sometimes more, each with, &c. 

Stamens, usually numerous. 

Carpels, numerous, without awns, &c. 
As tabular arrangements are hard reading, they may be 
relieved and lightened by remarks and illustrations, or by 
adding - information that properly takes the form of regular 
composition. 

12. Considerable nicety attends the exhibition of Differ- 
ences, there being, except in dichotomies, no regular 
method. 

Numerous examples have already been given of stating 
difference by pointed contrast. When more than two things 
are compared, this is impracticable. Still, the value of the 
pointed contrast, as appealing to the most fundamental sensi- 
bility of the human mind, should never be lost sight of. We 
may, for example, select for comparison among the numerous 

* Annual or perennial herbs, sometimes entirely aquatic. Leaves entire 
or more or less divided. Flowers usually yellow or white. Sepals 5, 
very rarely reduced to 3. Petals 5, or sometimes more, each with a 
thukened hollow spot at the base, often covered by a minute scale, 
btamens usually numerous. Carpels numerous, without awns, in a globu- 
lar or ooiong head, each containing a single ovule attached near its base. 



STATEMENT OF DIFIT.IM'.N 

species of a genus all the twos that are mosl lial 
founded. 

If the differing species of a -onus, or the differing 
a family, differed throughout ; that is, if no two 
thing but in the common features of the higher c 
pointed contrast would still be effective. Tims thre 
might be contrasted on a single feature, differing in all 
three. The actual case, however, is that differing have 

many partial agreements ; of six species, three maj 
some one point, four in another, and so on. In this state of 
things, we might carry out a little farther the exhibitii 
Agreements. We might give Nos. 1, 3, 4, 6, 
in certain features; 2, 4, 5, as agreeing in oth 
additional plan is to modify the statement of the generic 
ments thus : — Feature A is possessed by all except No. l' ; 
Feature B is possessed by 1, 4, 6 ; Feature C by 2, i. 
so on (adopting the tabular form). 

For example, Lindley constitutes an ' Alliance ' or Sub-cl 
Berberales, in which he places seven Natural Order.-, 
tinguished by the Flowers, Stamens, Pistils, &c. ; but 
partial agreements, thus — 

Flowers ; regular and symmetrical. All the seven, except 

Fumariaceaa. 
Placenta ; axile in four (naming them), parietal in two, 

sutural in one. 
Stamens ; alternate in four, opposite in (hree. 
Every device that brings clearly into the view either Agree- 
ments or Differences is vital to the understanding and thi 
collecting of the characters of the various classes. Whenever 
there is occasion or scope for the exhibition of agreement and 
difference, the manner of it should be prominent and i 
ostentations ; often the best course is to detach the si 
from the ordinary form of composition, and to put it in tabular 
array or contrast, as already exemplified. 

It is a rule of good exposition not to mix up thi 
of characters with reflections and theorii 
or explanations. This applies especially to all BO 
the descriptions are long and complicated. The followin 
an improper mixture of the two modes — ' The odours < 
as well as their colours, vary much. 17 
flowers are very obscure. T. 

of fragrant volatile oils in resins. Th ibttt 

nature as to elude chemical ano 1 ome How 

ferous only in the evening. This is the •" The sen- 



53S LOGIC OF ZOOLOGY. 



tences in italics should have been withheld until the facta 
respecting the prevalence of odours had been first stated. 

V. Index Classification of Plants. 

13. From the circumstance of passing through the 
Liunaean classification, so well adapted to the ready deter- 
mination of plants, Botany affords the best example of 
an Index Classification. 

We may retain for this purpose the Linnoean system in its 
literal form ; or we may have recourse to the modified schemes 
of recent Botanical writers. The principle is the same. Wo 
commence with certain characters, having alternative modes ; 
and the key or index informs us what classes each mode points 
to. A second character is then examined, its alternatives 
found, and the corresponding classes discovered. (See Lind- 
ley's Vegetable Kingdom, Benthain's British Flora, &c.) 

LOGIC OF ZOOLOGY. 

14. The difficulties of Zoological Classification relate 
to the multitude and the complication of the Animal King- 
dom. 

The multitude of the objects to be arranged, and the com- 
plication of even the lowest forms, distinguish Zoology from 
all other classificatory sciences. There are certain partial 
compensations. As compared with Minerals, the organs of 
Animals present numerous relations of concomitance ; and as 
compared with Plants, the Animal Kingdom falls in a remark- 
able degree, under a lineal series, or consecutive development. 

I. Characters of Animals. 

^ 15. We must look for the characters of Animals in the 
division of the animal system into constituent Organs. 

The Animal, like the Plant, is made up of Tissues and 
Organs, which have a certain amount of sameness, with 
variety, throughout the entire Animal Kingdom. The enu- 
meration of these belongs to Biology ; Connective tissue, 
Elastic tissue, Adipose tissue, Cartilage, Bone, Muscle, Nerve, 
Vascular tissue, Blood corpuscles, &c. In Zoology, however, 
the Tissues are viewed mainly in the Organs ; and Zoological 
characters are characters of organs. There is not the same 
use made of distinction of Tissue, as we have seen in Botany, 
lhe basis of Zoological Classification is the division of the 



COMPARATIVE ANATOMY AND ZOOLO 

Animal system into Organs. Those, with their f 
be variously arranged, there being two natural grt 
the Vegetative Organs and Functions (Nutritive and B 
luctive) — Digestion, Absorption, Circulation, Nutri 
Secretion, Excretion, Respiration, Generation, Develop!! 
(2) the higher Animal Orgaus — Locomotion, the I 
the Brain. 

In all these various organs, characters may be 
there being none but what are subject to variation thl 
the Animal series. The Anatomy of Vertebrates com 
the following parts :— Skeleton, Muscles, Brain and Be 
Teeth, Alimentary Canal and Appendages, Absorbents, Citt u- 
lation, Respiration, Urinary organs, Skin, Generative Organs. 
The Blood is also a source of distinction in the larger divisions — 
as between Vertebrate and Invertebrate, Warm-blooded (Birds 
and Mammals) and Cold-blooded (Fishes and Reptiles). 

The grand separation, common to all classificatory sciences, 
between the General and the Special Departments, in the 
Animal Kingdom, gives birth to the two subjects, — (Join pa ra- 
ti ve Anatomy and Zoology. As in Mineralogy, and in Botany, 
these should repeat and support one another, giving the same 
information in two different forms. 

The Comparative Anatomy arrangement, besides settling 
the selection and the order of Zoological characters, is a most 
powerful instrument of generalization. The exhibition of each 
successive organ in all varieties and modifications, discloses 
many aspects otherwise hidden; and places the more general 
and fundamental peculiarities in a strong light. Much of 
the insight that we at present possess regarding the brain is 
due to Comparative Anatomy. Too great pains cannot bo 
given to the perfecting of the Comparative Method ; and the 
grand secret is the lucid presentation of agreements and of dif- 
ferences. 

16. There being, in Animals, a numbei of distinct 
omans, a search is made for Laws of Concomitance 
tween them. 

It is a part of Biology, and an indispensable aid to 
to find out the correspondences or laws of concomil 
between the different organs— Moving Organs, Nervous 
System, Digestion, Reproduction, &c. 

These laws occur under various aspects. Some ar 
cal generalizations, such as the coincidence of the ruminant 
characteristic with the cloven foot and horns on the frontal 



^o LOGIC OF ZOOLOGY. 

bone. Other coincidences are mutually related, and are part 
and parcel of the development of the species ; as the advance 
of the brain with the muscular system, the reproductive 
organs, and tbe organs generally. The fact of increase of 
organization as a whole implies laws of concomitant advance- 
ment of all the leading organs. The connexion between an 
animal's organs and its circumstances or conditions of life is 
uot a law of co-existence, but of mutual implication; it does not 
rjve us two independent facts, but the same fact on two sides. 
All references to the element of each species — water, air, 
earth, the body of another animal — are to be held as merely 
illustrating the nature of the organs. 

The best established laws of concomitance in the animal 
organs, on which depends the existence of a science of Zoo- 
logy, as distinguished from a Comparative Anatomy of ani- 
mals, are liable to exceptions. Sometimes a single species 
will mar the unanimity of an entire Division, like Amphioxus 
among fishes. It is clear, however, that such exceptions are '' 
to be mentioned, and then disregarded. They do not even 
prevent us from supposing that the characters whose con* 
junction they violate are united by cause and effect ; for 
although causation permits no exceptions, it may be ocasionally 
counteracted. 

The more we can exhaust the relations of correspondence 
or concomitance, and the more precisely we can express them, 
the better are we prepared for the great classifying operation 
that makes up Zoology. The full import of the remark will 
appear under the next head. 

It might seem superfluous to insist on preserving a regular 
order in the statement of Characters throughout the whole 
scheme — whether in the Comparative Anatomy or in the 
Zoology, — seeing no one can follow out comparisons that are 
not uniformly expressed. 

II. TJie Maximum of Affinity as [jiving (he Classes. 

17. The choice of Classes follows the maximum of agree- 
ments in the several organs. 

The existence of Laws of Concomitance indicates the possi- 
bility of finding animal groups that agree in two, three, or 
more organs, or important modifications of organs. The 
zoologist grasps at this circumstance, in order to form his 
leading classes. 

In appearance, but only in appearance, there is another 



BASIS OF CLASSIFICATION. ;, j | 

principle of grouping. Some one organ 
of classification ; for example, the Reproductive 
gives the name to Mammalia. In reality, however 
is made not on account of the organ by itself, bu 
of the number of its alliances. 

An extreme supposition will place this fact in a oil 
light. Let us imagine that every one of the leading 
or systems, — Nervous, Reproductive, &c. — was wholly m 
nected in its modifications with every other organ ; thai 
nervous system might vary through all poa 
without any corresponding variation in any thing else. Under 
such circumstances, we might have a comparative anatomy of 
each organ, but no concurrence of organs. Zoology \\ 
be incompetent and non-existent. The only possible ola 
cation would be according to the Comparative Anatomy of the 
several organs. We might assign a superior dignity to 
same one organ, as the Brain, and give it apriority in arrange- 
ment, and a preference in study; but after the entire animal 
kingdomhad been exhaustively arranged under the compar 
anatomy of the Nervous System, the same operation v. 
have to be repeated under the other systems ; the work w 
then be finished ; being substantially the present science of 
Comparative Anatomy, without the relief that is at pn 
afforded, to the overwhelming mass of details, by laws of 
Concomitance. 

Accordingly, the justification of preferring one organ as the 
classifying basis, is avowedly its alliances. The taxonomic 
value of the ' placenta ' in Mammalia is the number of cba 
ters that it carries along with it. * Man, the Apes, th 
tivora, the Cheiroptera, the Rodentia, — are all as closely con- 
nected by their placental structure as they are by their general 
affinities^ (Huxley). The real motive to the grouping is noi the 
placental structure, hut the general affinities. 

We may make another illustrative supposition. If all the 
organs were strictly co-equal in development and in 
tions; if the Nervous System, the Muscular 
Reproductive System, &c, were all modified mstrici 
tance, there would be no such thing as a preference <• 
whereupon to base classification; the Reprodn 
could be no more a clue to the ' general affinities ' th m 
digestion, or the respiration. There would be no menti m of 
a special basis; general affinity would alone be prom 

It would appear, however, that the constitu* ai 
the animal organization are not co-equal and concomitant in 



5J-2 LOGIC OF ZOOLOGY. 

their changes ; some carry with them more, and some less, of 
general affinity or concomitance. Taking the whole Animal 
Kingdom, we tind that the Nervous System is by far the most 
important basis of classification ; the reason being that the 
organs generally cannot advance without a corresponding rise 
in the regulating and co-ordinating organ. There cannot be 
an extension of the muscular apparatus without an extension 
of the brain ; while the muscular apparatus itself implicates 
many other parts of the system. 

Next to the Nervous System is that part of Reproduction, 
embracing the mode of Development of the animal from the 
germ upwards. We have already seen how far this governs 
the divisions and sub-divisions of the Mammalia ; their very 
name is founded on it. 

If, for the sake of illustration, it were asked what would be 
the ivorst organ for classifying upon — the one that undergoes 
the greatest degree of unconnected or isolated variation, — thd 
answer would probably be the Heart. 

III. Classification hy Grades. — Species. 

18. It being assumed that each class is formed on the 
maximum of affinities, the number of grades is regulated 
by the occurrence of a succession of suitable groupings. 

The grades, or halting-places, are a relief to the burden of 
numerous common characters ; but there is no need to con- 
stitute them where the amount of resemblance is inconsider- 
able. 

In the higher Vertebrates, a succession of six, seven, or more 
grades is admissible and advisable ; while the attempt to con- 
stitute Natural Orders, Genera and Species, in the Protozoa, 
is misplaced and savours of pedantry. 

In Mammalia, the distinctions of Species may be numerous 
and important ; profound differences separate the Lion and 
the Tiger, the Horse and the Ass. In Birds, on the other 
hand, the species often turn upon small and nice peculiarities. 
Of the three hundred species of Parrots, it is impossible that 
there can be specific differences either numerous or important ; 
the Psittacos erithacus, for example, is distinguished as grey, 
with tail red! The domesticated varieties of the horse, dog, 
and cat, have wider differences than many species, or even 
genera, of the lower animal tribes. The differences between 
a fcegro and a Caucasian (varieties of the Species— Man) pro- 



I 



AGREEMENT AND DIFFERENCE. 



bably surpass in number the distinctions between two Natural 
Orders of Infusoria. 

In some cases, there occurs a single character so bold and 
remarkable as to satisfy our utmost demands for a specific 
distinction. Such is the extraordinary electrical organ in 
tain fishes. The species of the Gymnotus named electricu8 t is 
sufficingly marked by this single feature, in whose preft 
the describer abstains from all further specification. 
IV. Marking of Agreement and Difference. 

19. Zoology depends greatly on the rule of parallel 
array for Agreements, and of pointed contrast for Differ- 
ences. 

The characters of classes, high or low, should be thrown 
into the form most advantageous to the reader, that is, the 
tabular arrangement, with appended remarks and comment- 
aries in ordinary typography. 

For example, the characters of Aves (reckoned sufficient for 
discrimination, although inadequate as information) are these: — 
Reproduction : — oviparous 
Respiration : — air-breathing 
Heart : — four cavities, as in the Mammalia 
Integument : — feathers 
Teeth : — wanting ; substitute horny jaws 
Locomotive Organs : — the anterior limbs are wings. 
Besides these characters much is to be said as to the points 
of community, in the Nervous System, the Digestive System, 
and other parts. 

For the statement of Difference we may select Mr. Huxley's 
primary division of Birds into three classes ; an instance where 
the pointed contrast may be extended to three members : — 

SAURUB-ZB KATIT53 CARINATJJ 

Metacarpal Bones 
Not ankylosed Ankylosed Ankylosed 

Caudal Vertebrae and Tail 
Longer than body Shorter Shorter 

Crest of Sternum 

None Present 

Barbs of the Feathers 

Disconnected Connected. 
There are several other characters of the second and third 
classes, and no more of the first. Hence, we might have put 
the first against the two others as a whole, and then worked 
out the present contrast upon these two, 
24 



544 



LOGIC OF ZOOLOGY. 



Not merely in the formal exhibition of generic and specific 
characters, but in every incidental comparison of one class 
with another, the statement of Agreements and of Differences 
should always be clear, emphatic, and ostentatious. 

V. Index Classification. 
20. An Index Classification for Zoology might choose 
between the two alternatives — the tabular and the dielwtom- 

OILS. 

The Tabular method has already been suggested for Mine- 
ralogy, and will again be brought up for Diseases. The 
Dichotomous method is carried to perfection in Botany. 

A tabular plan could be based upon Comparative Anatomy : 
there being given, under every peculiar mode of each organ, a 
complete list of all animals possessing that mode. Thus,' 
there would be a table of the species conforming to each 
grouping of the Teeth, so that the discovery of such grouping 
in any given specimen would decide the animal as one of the*j 
list. A second character being noted as present in the speci- 
men would direct to a second list, where the animal must.J 
appear ; the choice is now narrowed to such as are common 1 
to both lists, A third, and a fourth character, being followed] 
out in the same way, would reduce the choice to still smaller 1 
limits; and eventually the enquirer would be guided to the 
proper Species. 

The dichotomous method of Botany, if fully adapted to 
Zoology, as it might obviously be, wouid be still better. 

The want of an Index is less felt in Zoology because of the: 
better marked specific distinctions, at least until we descend; 
to the inferior tribes, where there are numerous species, 
slightly marked. It would be pre-eminently necessary for 
Birds, among Vertebrate animals, and for the Invertebrate 
Orders generally. It is less necessary for Mammalia- except 
in a collection of unusually vast extent, 



CHAPTER VII 

LOGIC OF PBACTIOE. 

1. The Practical Sciences are defined by their 
I Ends. 

Medicine is the practical science having for its end Health. 
t Grammar and Rhetoric have for ends the perfection of the 
instrument of Language. 

2. There is one crowning end, the sum of all other ends, 
namely, Happiness or Well-being. 

People desire Health in order to be happy. There can be 
oo end beyond human enjoyment — the gaming of pleasure 
ind the averting of pain. 

3. The final end of all pursuit must be assumed or 
granted ; it cannot be proved. 

No proof can be offered of the position that Happiness is 
me supreme end of human conduct. We must be satisfied 
svitb. the fact that mankind make it the end. As all proof 
consists in referring the point in question to something more 
undamental, there must be at last something taken for 
granted on its own account. Such is Happiness, the 
crowning end. Men desire Happiness, either for themselves 
)r for others, as the goal of all endeavour. 

4. There is, however, a want of perfect unanimity as to 
;he final end. Some even deny that Happiness is the end; 
.vhile there may be great difference of opinion as to the 
.lature of the happiness to be sought. 

The end set up by some, as the final end of all, is Virtue. 
To those that embrace this view consistently, there is no 
^eply ; there is no possible appeal from a fundamental end. 

We may, however, enquire whether any class of persons do 
consistently and thoroughly maintain virtue, and not happi- 
less, to be the sole end of all endeavours. Wherever thi 
nconsistency, an argument is possible. 

Now, in reply to the setting up of Virtue, or more 
lenial, as an end, we may urge, first, that the conduct of I 
and shows that, in the great mass of cases, they regard virtue 



510 LOGIC OF PRACTICE. 

as a means to happiness. The virtue of Howard consisted nc 
in the fatigues and privations suffered from his journeys, an 
from visiting squalid dungeons ; it was in the amount of liuma 
misery that he relieved. 

condly, the position that Virtue is an end is almos 
uniformly coupled with the assertion that, in the long rur 
Virtue is" Happiness; which is merely another way of assigi 
inir Happiness as the end. 

Thirdly, the thorough carrying out of the position tha 
Virtue, in the form of ascetic self-denial, which is Virtu 
dissociated from Happiness, is the ethical end, would be tantr 
mount to abolishing the difference between good and evi 
with which virtue itself is identified. Virtue, in the sense sup 
posed, flourishes in misery ; the more miserable we are, th 
greater scopa we have for virtue; the more miserable w 
make other people, the more scope we give them for virtue. 

Again, Haj3piness may be allowed as the end, and yet ther 
moy be wide differences of view in the interpretation of th< 
end. The partizans of virtue may re-appear on this ground 
affirming that Happiness is only to be found in Virtue o 
Duty, not in enjoyment and in the absence of pains. Th< 
reply proceeds as before ; are these reasoners thoroughly 
consistent with themselves ? If they are, they cannot bi 
refuted ; if they are not, they may. 

Great variety of opinion may be held as to the beings whosi 
happiness is to be sought. Are we to seek our own happiness 
solely, or the happiness of others solely, or partly the one anc 
partly the ocher ? How far are w r e to extend our regards— 
to our own kinsmen, to our fellow citizens, to humanity ir 
general, to the lower animals ? In none of these points is 
argument possible, unless where people are inconsistent, which 
they need not be. We cannot reason a person into the adop- 
tion of other people's happiness as an end, unless such person 
has already of his own accord embraced some doctrine that 
involves this, as for example, the profession of Christianity. 
Neither can we offer any reason for extending sympathy to 
the lower animals. An education of the feelings is the only 
mode of enlarging people's sympathies. If o man can be argued 
out of a consistent selfishness. 



CHAPTER VIII 
LOGIC OF POLITICS. 

1. Politics, in the largest sense, refers to the action of 
luiiian beings in Society. 

The notion of Society can be gained only by each i 
ndividual experience. The first example of it is the Family, 
vhich contains a plurality of persons in mutual co-operation! 
vithcommaudandobedience. The earliest notions of an: li 
aw, command, obedience, punishment, superior, inferior, ruler, 
subject, — are gained from the various aspects of the 6 
lomestic circle. 

The larger aggregations of the school, village, parish, town- 
ship, church, &c, repeat all those aspects of the family, v. 
Iropping the incidents special to the family. 

2. The science of Politics, as a whole, is either Theoreti- 
cal or Practical. 

Under the Theoretical Science of Politics must be described 
;he structure or organization of Political Society; this I 
equally essential as a preparation for the Practical Sci< 
Ml the leading terms of Politics must be defined ; all the \ 
)f the Political system explained. To this preliminary branch, 
Sir G. C. Lewis applies the designation ' Positive Politic 

In the second place, the Theoretical Science traci 
ind effect in political institutions, as facts of the ord( 
lature; in the same way as Physics and Chemistry describe 
iause and effect in inorganic bodies, and Biology in Living 
3odies. The theoretical department of Society would state, 
ipon evidence of fact, conjoined with reasonings from human 
lature, what are the consequences of given ins: 
mote from Sir George Lewis : — 

1 It assumes that we know what a state is ; whn I 
vhat are the conditions necessary for its existence; by what in- 
struments it acts; what are its possibl 
Starting from this point, it inquires how certain 
nerd, and certain laws and political in 
'rom observed facts and from known principles of human 
•o determine their character and tendency ; it i 
propositions respecting their probable con Bide 



548 LOGIC OF POLITICS. 

versally, or in some hypothetical state of circumstances. Thus i 
may undertake to determine the respective characters of monarchy 
icracy, and democracy ; it may show how each of these form 
•verament promotes the happiness of the community, an< 
which of them is jirc/t-rable to the other two. It may inquire into th< 
operation of certain modes of preventing crimes — as police,— o 
criminal procedure, and of legal punishment, such as death, trans 
portation, imprisonment, pecuniary fines,— and it may seek t< 
determine the characteristic advantages and disadvantages of each j 
in certain assumed conditions. It may inquire into the ojzieratioi I 
of different systems of taxation — of laws respecting trade anc 
industry— of modes of regulating the currency — of laws regulating 
the distribution of property with or without will — and other 
economical relations. It may lay down the conditions whici 
render it expedient to govern a territory as a dependency ; 01 
which tend to promote the prosperity of a new colony. It may 
define the circumstances which ensure the permanence of national 
confederacies, and it may inquire what are the rules of interna- 
tional law which would tend to promote the uninterrupted main- 
tenance of peace. 

' It seeks to lay down general theorems respecting the operation 
and consequences of political institutions, and measures them hy 
their utility or their capacity for promoting the welfare of the 
national community to which they are applicable. Propositions 
of this sort may lead (though not by so direct a road as is often 
supposed) to preceptive maxims ; but they are themselves merely 
general expressions of fact, and they neither prescribe any course" 
of conduct, nor do they predict any specific occurrence ; though, 
from the generality of their form, they may relate as much to the 
future as to the past.' 

The Theoretical Science of Society is sometimes expressed 
as the * Philosophy of History/ or the accounting upon general.! 
principles of cause and effect for the actual course of political! 
events, tlic growth of institutions, the progress and decay of j 
nations. History, in the ordinary signification, recounts these 
things in the detail ; the Philosophy, of History generalizes the 
agencies at work, and endeavours to present the whole as fol- 
lowing out certain great leading ideas. A few writers have 
aimed at establishing such generalities — Yico, Montesquieu, ; 
Millar, Condorcet, Auguste Comte, &c. 

Practical Politics consists of maxims of political practice. 
Here we have to suppose an end, — the welfare . of the com- 
munity, or any other mode of stating the political end. 

This necessarily appears with more or less prominence in all 

political treatises. Aristotle's work is a search after the best 

nment. Machiavel's treatises are preceptive or practical. 

Locke does not formally enquire after the best constitution, 



SCIENCES COMHUSED IN POLITICS. 

rat under the guise of what is necessary to heinsinn 

■ertain political forms, and certain legislative princip] 
Sound method requires that a writer should, in 
nstance, separate the Theoretical from the Practical. 

3. The entire department of Political Science at the | 
sent day comprises several sciences. 

It has been found practicable and convenient to with : 
'rom the wide region of human society, certain subj< 
;an with advantage be cultivated apart, and thus to reduce the 
complication of political enquiries. 

(1) The first of these is Jurisprudence. This is a distinct 
Dranch bearing" on the form of Law, as apart from its Bubsta 

[t teaches how laws should be expressed, with a view to their 
satisfactory interpretation by the Courts ; it embraces evidei 
ind the principles and procedure for the just administration 
:>f the laws. It does not consider the choice and gradatio 
punishments, but explains how they should be legally defined, 
io as to be applied in the manner intended by the legislator. 

(2) International law is the body of rules agreed upon by 
independent nations for regulating their dealings with each 
3ther, both in peace and in war. It includes, for example, 
questions as to the Extradition of Criminals, and the right of 
Blockade at Sea. 

(3) Political Economy, or the science of the production and 
distribution of Wealth, relieves the political philosopher of a 
considerable part of his lead. The legislation regarding Pro- 
perty in Land, Trade, Manufactures, Currency, Taxation, &C., 
is guided by the enquiries of Political Ecomony. Withii 
own sphere, this science has the same logical character ac 
mother science. It has its definitions, its principles or I 
partly inductive and deductive, and its methods, which 

the ordinary logical methods. 

(4) Statistics is a branch of the Science of Society, adi 
ting of being cultivated separately. It furnishes the : 
data of political reasoning in the most complete and auth. 
form. 

4. The subjects remaining to Political Sci 

the Form of Government, and (2) Legislation on all t 
not otherwise embraced. 

The different Forms of Government, their prcci I 
lion, and their several tendencies, constitute the 
problem of the political science. The discussion of M 



550 LOGIC OF POLITICS. 

Aristocracy, Democracy, enters into every treatise called 
political. 

In immediate connexion with this snbject, if not a part of 
it, is tbe distribution of the functions of government, into 
Legislative, Administrative and Judicial ; the delegation of 
the powers of government to subordinate authorities, as in 
provincial, local, or municipal government. 

These subjects are sometimes considered as exhausting the 
sphere of Politics ; but in a very narrow, although distinct 
signification of that sphere. Thus, Mr Mill remarks, — ' To 
attempt to investigate what kind of government is suited to 
every known state of society, would be to compose a treatise 
on political science at large. 9 

It must, however, be matter of enquiry how a government, 
when constituted, is to discharge its functions. This supposes 
that tbe functions aro classified and defined ; an operation 
involving one very important enquiry in Politics, namely, the 
proper Province of Government 

There are certain things that Government must undertake, 
in order to fulfil its primary ends ; such are Defence, and 
the Preservation of Life and Property. 

There are other things tbat government may or may not 
undertake — as the Support of Religion, Education, Postal com- 
munication, the maintenance of Roads, main Drainage, and 
other works of general utility. 

5. The curtailment of Individual Liberty is a necessary 
effect of government ; and the degree of this curtailment 
is a vital consideration in Political theory. 

In order tbat men may act together in society, each must 
in part subordinate their own actions and wishes to the 
general^ scheme. Obviously, however, individual liberty, 
which is in itself a chief element of well-being, should be 
restricted in tbe least possible degree ; and tbe burden of 
proof must always lie upon the proposer of restraint. 

TJie Structure of Political Society. 

6. The preliminary branch of the Social Science, con- 
tains the Definition of Political Society, and of all the 
Relationships and Institutions implied therein. 

This is the part of the subject entitled by Sir G. C. Lewis 
Positive or Descriptive Politics. It teaches wbat is essentially 
involved in the idea of political government. It explains the 



TIIE POLITICAL BTR1 

necessary instruments of government ; as a la 
obligations, sanctions, executive c mmands, and tho like. [| 
ter enquires into the opera! 

one to others (Practical I\ 

monarchy, aristocracy, democia 

is the best form. It shows what is 

but does not say which punishments are the 

It expounds the relations of master and fri 

er and slave, bat does not tr. ce their U 
.re of the parties concerned. It ex 

dependency, without arguing the question — Should c 

have a separate government. It shows what are t, 

constituting an exchange, and the differ* 
E and a money equivalent, but does not dwell upon the adv.. - 
; tages of exchange in facilitating trade. (Methods of 

in Politics, vol. I., p. 54J. 

The fundamental notions of Political Society — 
1 Law, Command, Duty, Sanction, Obligation — are I of 

I by John Austin as a part of the special of Jarisj 

dence. That these notions are at tne basis of Jurisprudence 
j is beyond doubt. Still, in a completely formed P 

Science, they would be given once for all at the outset, under 

the head of the Structure of Political Society, and would m 
i only to be referred to by the Juris 

The very fact of Political Society involve 
primary notions ; forming a mutually implicated, or corre- 
lative group. 

ernmcnt. — This is the essential fact of political society ; 

I to define it, or any one of its numerous synonym- — y 
Authority, Ruler, Political Superior — is to define p 

; society. The definition must be gathered from the I 
common to Political Societies. It is given by S 
as follows : — '" When a body of persons, yielding obedience to 

jr no superior, issue their commands to certain other persons to 
do or to forbear doing certain acts, and threat the 

disobedience of their commands by the inflicti 
are said to establish political or 

Closelv examined, this definition c 
be defined — for example, superior and command — 
not a definition suited to inform the ignorant, [t ifl rather 
the nature of the first definitions of geometr] :lo, 

&c.) which do not communicate notions, but i to 



552 LOGIC OF POLITICS. 

fix with more precision the boundaries of notions already 
gained from experience. We should require, in the first 
place, to know political societies, in concrete instances; and 
the definition would teach us the corresponding abstraction or 
generality. 

Austin (Province of Jurisprudence Examined) endeavours 
to build up the definition from its simplest assignable elements. 
Starting with Command, he defines this as ' the expression or 
intimation of a wish, to be followed with some evil, if not 
complied with.' This involves only such facts of human nature 
as wish, expression, non-compliance, infliction of evil. In the 
notion of Command, as thus defined w-e have nearly all that 
is signified by Government, Sovereign, Superior, Authority. 
We have only to specify the persons intimating the wish (to 
some other persons) and following up the non-compliance with 
the infliction of pain. 

The supposed command is a Law. The evil to be inflicted 
is a Sanction, Penalty, or Punishment. The persons addressed 
are Subjec's, Inferiors ; they are placed under Obedience, Duty, 
Obligation. The aggregate of persons comprised w T ithin the 
scope of the same commands, is a Political Society, a Community , 
a People. They are in the Social state, as opposed to the state 
of nature. 

Moral Eight and Wrong must be referred to the same com- 
plex fact. 

8. Government is usually said to have three distinct 
functions — Legislative, Executive, and Judicial ; each one 
giving birth to a numerous class of notions. 

Legislature. — The power of making general commands uni- 
versally applicable, under given circumstances, is called 
Legislation ; it is the most extensive and characteristic func- 
tion of government. The process is very different under 
different forms of government. In every shape, there are 
implied as subsidiary notions — statute, and its synonyms, pub- 
lication or proclamation, enactment and repeal,"&c. 

Executive, Administration, — Implies performance of the speci- 
fic acts occurring from day to day, in the exigencies of society 
— organizing and directing the military force, negotiating with 
foreign governments, appointing the officials of government, 
erecting public works, &c. In this function, the government 
is said to use ministers, to issue orders, to receive and issue 
despatches, reports, to superintend all functionaries. 

Judicial.— A distinct function of government, usually en- 



THE POLITICAL BTltUCTl 

trusted to *a separate class of persons. It 

ments to the commands and operations of government, e 

in the way of misunderstanding, or of difi 

are removed by Judicial Institutions, calle I I 

presided over by Judges, said to admin: 

to a definite Procedure, and rules of Et 

arrangements belonging to these several heads are detailed and 

defined by the special science of Jurisprudence. 

With all varieties of government there must ex- 
three functions ; in rude governments, they are 
the same persons ; in civilized governments, they are I 
or less divided between different persons. 

9. Under 'Form of Government/ there is a numb 
structural modes, for which there are specific ddsigual 

The Form of Government brings out the designate 
Monarchy, Aristocracy, Democracy, Republic, Mixed Govern- 
ment, Balance of Power, Constitution. 

The logical division of Forms of Government is into tho 
government of one person (Absolute Monarchy) and the govern- 
ment of more than one {Republic or Commonwealth). It, in 
the second alternative, the governing body is small, the 
government is an Aristocracy ; if the power is lodged in the 
majority of adult citizens, the government is a I' 
Such names as Limited Monarchy, Constitutional Monai 
mean either Aristocracy or Democracy; they indicate 
form of monarchy, but the reality of another power, A 
Mixed Government is a mere semblance ; some one of the con- 
stituents is in point of fact the sovereign. 

Aristocracv, where it prevails, makes a division of the 
people into Nobility and Commonality. Often the govw 
body is a hereditary nobility. 

Representative Government, the growth of modern Do: 
is a leading notion of Political Science. The meanio 
the whole people, or a large portion, exercise the ultimate 
controlling power, through the deputies periodically i 
themselves. In the ancient republics, the corporal 
legiate action lay with an assembly of all the citizens, 
many as could be got together. 

The operations of corporate government give bir 
political elements expressed by assembly, del 
debate, decision by a majority, chairman, election, 

10. The Functions or Business of government introduce 
many structural elements. 



554 



LOGIC OF POLITICS. 



The first function of a political society being defence, there 
is a large institution corresponding, called the War Organiza- 
tion — Army and Navy. 

The protection of the members of the society from one 
another is either by an application of the War force, that 
is the soldiery, or by a separate force called Police. 

These two leading institutions involve many others. An 
official machinery, or bureaucracy, is interposed between the 
sovereign power and the actual instruments. For paying the 
cost, there must be a levy of Taxes, with a bureaucracy ! 
corresponding. 

If the government undertakes public works — roads, bridges, 
public buildings, means of communication — it becomes a sort of 
industrial management on the large scale. 

The coining of money is a proper function of government. 

The regulation of bargains and contracts of every description, 
as well as the enforcing of them, is a matter for the state. The 
marriage contract, in particular, the relations and rights of the 
different members of the family, are under state control. 

A Church Establishment, whether incorporated with the 
civil government, as is most usual, or existing apart, is a vast 
social machinery with elements and terms corresponding, all 
admitting of definition. 

11. In a society spread over a wide territory, there must 
be a division into local governments, duly subordinated 
to the chief or Central Authority. 

This originates the terms Central, Centralization, and Local, 
Provincial, or Municipal government and institutions. A small 
locality may represent in miniature nearly all the features of 
the entire society. The delegation of power to the locality 
may be small or may be great. Moreover, the Form of 
Government of the entire cociety repeats itself in the localities. 
If the sovereign is an absolute monarch, the local authority is 
absolute in the local sphere ; such is the oriental satrap, and 
the viceroy of the absolute European monarch. 

12. The Province of Government marks the line between 
Public and Private management. 

The habitual industry or every day avocations of the mass 
of the people must be left to themselves. Their manner of 
subsistence, their recreations and amusements, are also their 
own choice ; although governments have often interposed to 
regulate all such matters. 



ORDER AND PROGKES& 

j : 13. The mutual bearings of Public and Private fastita- 

< tions are so numerous, that a statement of the Polil 
structure is incomplete without the Private [nstituti 

The Industry of the People is an important element of the 
state politically. So are their Recreations, Tastes, Opin 
Literature, and Science. However much the government ab- 
stains from control in these matters, its operations in its pi 
sphere are influenced by every one of them. An agricultural 
community gives a peculiar character to the entire aetii 
its government. A community largely occupied in foreign 
trade involves the government in relations with foreign c 
tries. 

14. The good or ill working of the Political system 
leads to a variety of situations, requiring the consideration 
of the political reasoner. 

When the government fails to accomplish its main functions 
—defence, protection, justice, &c. — it receives the designations, 
'bad government/ ' mis-government.' Its badness may con- 
sist in partiality to individuals, which is injustice ; in not 
adhering to its own published regulations; in the capricious 
introduction of changes ; in preying upon the community by 
exactions, or by affronts, 

When. the government is excessive in its restraints on indi- 
vidual movements, it is called despot ical, tyrannical, opprei 
and the re-action or revolt is Political Libert//. When it 
meddles with what might be left to private management, 
said to over-govern ; the euphuistic phrase is & paternal govern" 
ment. 

The emphatic expression Social Order means, in the first 
place, that the government, whether good or bail, is obeyed ; 
the opposite state is Anarchy, Revolt. 

Order is also contrasted with Progress, Improvement, or 
Civilization. Those things that maintain the existing structure 
in its integrity are said to minister to Order ; while the a 
cies that raise the society to a higher pitch of improves 
are said to minister to Progress. In point of fact, thi 
tion between the two is very slight ; what ifl goofl for oi 
with very trifling allowances, good for the other (Jlill'i h!#- 
presentative Government, chap. II). 



ggg LOGIC OF POLITICS. 

THEORETICAL POLITICS. 

15. The Laws, Principles, or Propositions, of political 
8 i liety, together with the Methods of Investigation, consti- 

rheoretical Politics. 
The foregoing head, including the Analysis of the Social 
Structure, the meaning of State of Society, the Motions of 
Politics— is preparatory to the enunciation of the Laws of 
Society, so far as known. These Laws are best discussed in 
the theoretical form ; they may afterwards be changed into 
the practical or preceptive form, that is, into maxims of the 
Political Art. 

16. The Laws of Society may be either Laws of Co- 
existence, or Laws of Succession, of the different parts of 1 
the Social Structure. In both cases, they are laws of 
Cause and Effect. 

The complex structure of Political Society involves many 
relationships of Co-existence and of non-coexistence. Some 
arrangements always carry with them some other arrange- 
ments ; some thing's are repugnant to other things. The re- 
mark was made by Volney that the ' plains are the seat of 
indolence and slavery, the mountains of energy and liberty.' 
But whatever co-existences and repugnances can be predicated 
generally are dependent on causation. 

Again, we may take any one part of the social structure as 
a cause, and lay down the laws of its effects ; as w T hen we 
describe the consequences arising in a given state of society, 
from an absolute monarchy or from a state church. 

We may even take up an entire state of society, with all its 
mutual actions, and endeavour to trace its future destiny. 
This is the large problem of the Philosophy of History. 

Eat for devices of simplification, such problems would be 
wholly unworkable ; the complication of elements could not 
be embraced by the human mind. We should need to fasten 
upon some single agency, either comprehending, or outweigh- 
ing the others, whose solitary operation will give the key to 
the entire problem. The state of opinion and enlightenment 
of a community is an example of those over-mastering cir- 
cumstances. 

Human Character as a Political Element. 

17. As the subject-matter of Political Science is human 



POLITICAL ETHOL 

beings, the characteristics of human 
primary element. 

If all human beings were alike, either wholly or In tl 
points concerned in political action, the construction 
political society, whether easy or not, would be 
blem. But there are wide differenc 
of character essential to the working of the poli 
The differences between an American Indian, a Hind 
Chinaman, a Russian, an Englishman, an Irishman, n 
taken on the average, are such as to am 
lore and the workings of political institutions. ( riven 
Form of Government, or a certain constitution of 
Property, the tendencies w T ould alter greatly 
various types of character. 

The theory of Society consists in stating how hum; 
will act under a given social arrangement; it is, tl 
essentially a special application of the laws of mind and i 
acter. Hence a thorough knowledge of whatever Psych 
can teach would be a preparation for this study. 

Yet, all parts of human nature are not equ 
political action; the ethical qualities of Honesty, Ind 
Steadiness of Purpose, are more vital than the Artisl 
bilities. 

Moreover, Politics is concerned only with the cbara 
that appear in collective bodies. The politician ha. 
account all those individualities that are merged when men 
together in a body; that is, the qualities occ 
in scattered individuals and in minorities. Whi tonal 

character is a much simpler phenomenon than indivi 
character; as the flow of a river in ma— pier phj 

problem than the molecular adjustments of the liqu 

18. A Political Ethology would be a modifii 
character, consisting (1) of a selection of the qua! 
appear in national character, and (2) of the laws 
operation, 

(1) Following the divisions and 6ubdivisi 
as formerly sketched (p. 518), we should bav< 
prominence all that arise in human i 
collectively. 

Thus, to commence with Action, in the 
Energy. Prior to an account of the 
induce men to activity, there is a notable pecuJ 



55S LOGIC OF POLITICS. 






racter in the degree of the energetic disposition itself. Now jl! 
this shows itself, as high or as low, in whole nations, and is of 
importance as respects both the Form of Government and 
many other political arrangements. The inhabitants of tempe- 
rate climates are superior in natural energy, irrespective of all 
modes of stimulation, to the dwellers either in the tropics or I 
in the arctic circles. The English and Anglo-American 1 
peoples are probably at the top of the scale. 

Now this attribute has numerous social bearings. It favours 
private industry and the accumulation of wealth, an effect 
leading to many other effects. It is both directly and indirectly 
hostile to monarchical or despotical rule, and is, therefore, the 
parent and the guardian of liberty. 

In like manner, we might survey in detail the Feelings, 
Sensibilities, or Emotions of the mind, and mark those that 
have social significance, and those that appear in men col- 
lectively. Thus, the Tender Sentiments, or the Sociability of 
the Mind, when strong, draw human beings together in society, 
and favour the cohesion of states as well as of families. Again, 
the strength and the mode of the Sentiment of Power may be 
a collective peculiarity, w r ith national consequences. The 
conjunction of tender feeling, as patriotism within our own 
nation, with the love of domination beyond, is a peculiarity 
often repeated. 

The Intellectual qualities that stand out in national pro- 
minence are too numerous to be touched upon. It was an 
intellectually minded people, the Greeks, that began all the 
civilization flowing from science or philosophy. There is a 
certain depth of ignorance and incapacity that renders the 
higher modes of Political society impossible. A signal failure 
in either of the intellectual virtues — prudence and sympathy, 
is incompatible with political union. 

(2) The next part of Political Ethology is an account of the 
tendencies of these various characteristics, and of the means 
whereby they themselves are modified. The general science 
of character embraces this investigation on the wide scale, and 
the present department is a special application of the principles. 

Propositions of Theoretical Politics. 

19. The Political Structure, or Organism, being defined, 
the Laws of Theoretical Politics are the laws of Cause and 
Effect, traceable in the working of the several Institutions. 

What are the consequences of Absolute' Monarchy, or of 



CAUSE AND LI i 

Democracy; of Castes; of Entails; of Free T 

Laws; of Indissoluble Marriage; of State 1 

are a few of the enquiries of Political Science; tl 

enquiries of Cause and Effect. Given any of the 

as causes, the effects may be sought. Again, given 

ns the repression of agrarian crimes, the impartial admin 

tion of justice, the encouragement of trade,— we may 

causes. This is really the same problem in a d 

To all intents and purposes, the one enquiry is— CJivi D a C 

required the effect ? 

It is not uncommon for political philosophers 
such problems, as What are the effects of Monarchy, 
racy, Democracy, in general; what are the effects of 
in general, that is, under all circumstances, under every possible 
variety of human character. Now, with such strongly-ac 
causes as Absolute Monarchy, there may be ass rtain 

universal tendencies so decided as to be seldom wholly 
There are points in common to the despotism of a single p 
in all countries and times. The possession of power, wli 
on the great scale or on the small, operates with remarkable 
uniformity. This is a psychological tendency wh 
course is best seen in politics; where, by the necessiti 
the case, individuals have to be entrusted with power 
large amount. The same consideration renders the \ 
of slavery uniform to a high degree. 

20. The Propositions of Political Science rai 
two extremes; on the one extreme are propositions affir- 
ming universal tendency, and, on the other. 
affirming specific effects in limited cases. 

(1) The propositions affirming a universal tendency are 
exemplified above. Similar propositions may be found 
ing every institution of human society. In many institnl 
however, the tendencies are difficult to find out, and at 
liable to be defeated by other causes, that their 
has scarcely any value. For example, the 0] 
or privileged corporations, admits of no defiii 
with reference to all possible circumstances. '1 
land into large or small properties may ha\ 
in different social states. 

Nevertheless, the attempt should be d 
tendencies both of the Forms of Government 
varieties, and of all the leading Institution 
legislative action. It is equally indispensah 



5G0 



LOGIC OF POLITICS. 



precise worth of this class of propositions, to be aware of their 
infirmities, and of the cautions needed in applying them. 
There are prevailing tendencies of every important Institution ; 

f the Succession of Land, of Direct or Indirect Taxation, j 

of Religious Endowments, and the rest. The affirmations re- 
specting these are only probable ; they afford a certain pre- 
sumption of what will actually happen in individual cases. 
The special departments — Political Economy and Jurispru- 
dence — share the burden of these difficult problems. 

(2) Propositions confined in their range to limited circum- 
stances, to a narrow field of observation, may be so qualified 
as to state the causation with almost perfect exactness. Thus 
if we confine our views to communities in similar climates, of 
the same race, of nearly the same advancement in general 
intelligence, we can formulate with comparative precision the 
tendencies of a given institution, whether the Form of Govern- 
ment, or any of the other leading social elements. These 
Limited or Partial Theories are the really valuable parts of 
Political Science ; they afford the guidance in the art or prac- 
tice of Politics. 

With a view to these propositions, there must be a division 
and subdivisions of communities into classes. An example of 
such a classification is given by Sir G. C. Lewis, as follows: — 

' One large classification of communities for the purpose of 
a common predication is — 1, those communities which are in 
a wild and unsettled state, such as the African and Indian 
savages, the Bedouin Arabs, the JNbmad Tartars ; 2, those 
Oriental communities which live under a regular political 
government, but whose social state is nevertheless fixed and 
unprogressive, such as the Turks, the Persians, the Hindus, 
the Chinese, the Japanese ; 3, Christian communities partaking 
of the modern European civilization.' 

Setting aside the first class, as affording too limited a field 
for political data, Sir G. C. Lewis institutes a comparison and 
contrast between Oriental and European communities, showing 
the numerous important peculiarities that may be affirmed of 
each of the two classes as a whole. The following are some 
leading points of the contrast. 

Oriental. European. 

Government. 
Despotical Free 

By Delegation Direct from the centre 

International Law. 
Eude Intricate, forming a bal- 

ance of power 



LIMITED OR PABHAL Til 



Interwoven 

Polygamy 

Secluded 

Sialics of tl 
Slavery Oil m 

PunisJm 
Cruel MM 

Loose Closely fitting 

Alphal 

Intricate Simple 

Jbrw or Lit 
Poetry and mystical prose Argumentative pr* 
Numerous propositions of Cause and Effect could bt 
down respecting these peculiarities, connecting I 
one another, and with the Climate and Physical 
Physical and Mental Constitution, and the Ilistori 
cedents of the oriental races. 

Methods of Theoretical Politics. 

21. As in all other sciences, there must be Ob. 
of Facts. 

In Political Observation, there are special peculiari 
amenable to logical canons. The education of a 
observer is scarcely in any degree, as in the pbys 
an education of the senses; it consists mainly o( intelU 
habits. 

22. The Facts of Politics coincide with authentic B 
tory or Narrative. 

The individual occurrences that, when gener :iko 

up political principles, have to be correc 
the circumstances essential to the linl 
sequence of events in a revolution must be 
they occurred, and in sufficient fulness to give the OOOdil 
of cause and effect. 

The rules of historical evidence 8 
Logic, and as such they are given 
They have in view principally the nun 
the testimonies needed to establish the truth 



5C2 LOGIC OF POLITICS. 

A farther exercise of discrimination is requisite in the political 
historian, namely, to include all the circumstances entering 
into the chain of causes, and to separate accompaniments 
that have only a poetic interest. To do this, the his- 
torian must be himself a political philosopher; he must 
know that the dazzling glitter of spears in the sun has nothing 
to do with the fighting strength of an army, that the stature, 
complexion, voice, or dress of Charles I. had no bearing upon 
his quarrel with his parliament. In short, as regards the 
relevance of flic ts and circumstances, the narrator must under- 
stand what it is to trace cause and effect in history. ' In 
order to frame a coherent narrative, some theory of causation 
is necessary ' (Lewis). 

23. In Politics was first developed the reducing of 
observations to the form called Statistics ; definable as the 
observation, registration, and arrangement of such facts as 
can be given in numbers. 

The cultivation of statistics was first owing to the impetus 
given to political economy by the French economists ; it being 
possible to state in numbers the most material facts regarding 
trade, currency, taxation, production, population, &c. The 
subject now comprises matters relating to all branches of 
political observation ; Population, Births, Marriages, Deaths, 
Occupations, Diseases, Crimes, Pauperism, Education. 

Statistics gives an entirely new precision both to Theoretical 
or Speculative Politics, and to the operations of government. 
The increase or diminution of pauperism or of crime, in a large 
country, could be judged only in the vaguest manner without 
statistical returns from the officials concerned. The govern- 
ment would be at the mercy of accidental displays, and of 
circumstances where the impressions are exaggerated. A 
bread riot in a particular locality, an outrage of appalling 
accompaniments, would distort the judgment of the nation, as 
to the general state of destitution or of crime. 

24. The causes of erroneous observation in Politics, are 
partly common to the sciences generally, and partly special 
to the political science. 

Indolence and inattention, the love of the marvellous, 
aesthetic likings and dislikings, the support of a favourite 
theory, are operative in politics as elsewhere. The more 
special sources of bias in the political department are admira- 
tion of individual actors, party feeling, and, where practice is 



POLITICAL EXPERIME 



3C3 



concerned, direct personal interest. A 
these corrupting motives extend the 
iaing no less than to the observing 

Politics deals with human beings, w 
are in the mind ; while obsen 
appearances, from which the mental si 
inference. The right performance of 1 1 
is an operation based on Psychol. >j 
of Inductive Logic. That Charles!, v, 
the motives of Cromwell and the 1' 
are a matter of difficult inference ; requiriD ; 
of human nature (veracity, bias, &c), t 
and did in connexion with the fact. The secrecy of 
is the characteristic of many ethical maxims. 

Experiment in Polii 

25. Experiment, in the strict scientific meaning* ifl 

ally regarded as inadmissible in Politics. Tn 

are (l)the sudden introduction of extraordinary inilu -nces, 

and (2) the practical operations of government. 

It is not possible to submit a society to the pr 
ployed in studying a metal, or in detecting the law 
or Magnetism. A political community cannot be manipul I 
with a view to excluding artificially this or th.. 
lating it from all but known circumstances. 

(1) Some of the advantages of experiment a 
through the introduction of a new and extraordinary in i: I 
into the society — such as a famine, a common 
insurrection, an epidemic, an invasion, a new inv ■ the 
steam engine, a religious revolution. The Irish ; mine 
of 1845, is adduced by Lewis as a casein point The inll I 

of this terrible calamity laid bare the evils in tl. E tho 

Irish poor, and disclosed the secret springs in the B 
economy of the people, as effectually as could ha 1 lone 

by an artificial experiment contrived for ti. 

(2) It is the very nature of government, i 
proving government, to be trying experiments. E\ 
law is an experiment. There being an object I 

by the law, the public is supposed to be inter 

the effects of the me i A Police is 01 

effects upon crime observed. A Pc 

the consequences traced. So e 

agent in society, which is followed by defi l u0 



504: LOGIC OF POLITICS. 

experiments are not always free from ambiguity ; there may 
be concurring agencies either defeating or exaggerating the 
results ; hence a demand for the precautions of the various 
Inductive Methods. 

Causation in Politics. 

2G. In Political Causation, the predominating fact is 
Collocation ; there is seldom, yet occasionally, an appeal 

to Conservation. 

A political sequence is always immersed in a host of arrange- 
ments, positive or negative ; and although impelling forces 
must always be present, the result is dependent in a pre-emi- 
nent degree upon the direction given to these forces. Thus, 
a political rising depends less upon the greatness of an impel- 
ling force, than upon the direction given to forces always 
present. The demand for thirty shillings of ship money from 
John Hampden was the turning point of the English Revolu- 
tion. 

Yet in dealing with human nature, whether as individuals 
or political masses, any omission to allow for the principle of 
Conservation, in the form of Limitation of Human Energy, 
will lead to mistakes. Thus, a politician that would expect 
an Art-loving people like the Italians, Germans, or French, to 
take* on the energy of the English in business and in politics, 
without becoming less artistic, would be guilty of overlooking 
the law of Limitation. 

27. In Political Causation, it is especially necessary to 
keep in view the entire aggregate of conditions, positive 
and negative, entering into the cause. 

"When Luther preached against Indulgences, and when 
Hampden refused to pay ship money, these were merely a single 
condition out of a large assemblage concerned in bringing 
about the great events that ensued. Hence, the historian 
considers it requisite to describe the whole of the surroundings 
in the state of society at the time, but for which the conse- 
quences would not have arisen. 

To seek the cause of a political event in a single cir- 
cumstance is a perversion of the political problem. The 
most enlightened reasoners and historians are accustomed to 
state the case as an enquiry into the causes of a phenomenon. 
The phrase is not strictly correct ; the entire aggregate of 
antecedents is properly the cause; but as bringing forward the 



DEFECTS OF THE METHOD OF A< IT. 

idea of plurality of circumstances, conditions, or col 
the mistake is on the right side. The causation 
Revolution was a vast aggregate of prior arrangemenl 
state of the French nation, together with nun, 
stances in the world at lar^e. 

The Method of Agreement in 1 

28. The Method of Agreement enters i; 
investigatioD. but not without shortcomings. 

Like every other inductive enquirer, the political i 
first collects his facts; then compares them with a 
attaining laws of concomitance, which he farther v< 
Agreement, as a method of Elimination. 

This has always seemed the obvious course. Wi 
totle enquires into the effects of Despotical or of 
government, he collects examples of each, and looks onl 
the attendent peculiarities. By an inductive determin 
founded on Agreement, we are accustomed to conne 
ent forms of government with lower or with higher 
civilization. 

The first peculiarity of the inductive problem i 
affecting the sufficiency of the Method of Agreement, i 
mere number of concomitant circumstances in a Mute of 
society. The cause A, say Despotism, works in conjunc 
with such a large variety of other circumstance, — cli 
race, history, institutions in detail — B C D E -that 

we can hardly find in the whole area of our experience a 
sufficiently diversified series of instances to eliminate 
and find A followed in every instance by a. 

Worse than the mere number of accompanimcir 
of causes with intermixture of effects. Whatever I 
really flow from Despotism — whether discoi. 
tions, or the repression of men's energies and 
prosperity and progress — could flow from othi 
the effect a, an actual effect of A, might ah 
C, F, H. This would not prevent a 
with A ; it would rather in some 
bundantly present ; vet, as proving too much, it . 
to the evidence. An apparently more paralyz 
be, when the effect a, properly belonginj 
by some accompanying agent D ; one i 
occurrences in politics. Hardly any. 
is better substantiated than the disc 



5G(J LOGIC OF POLITICS. 

activity generally ; yet this did not follow at once on the 
imperial despotism of the Roman Empire ; the prior impetus 
acquired under free institutions was for a long time unspent. 
So, a law designed to produce a certain effect, may really be 
acting as intended; but the effect may be frustrated by 
evasions, or by passive resistance to its enactments. Restric- 
tions on trade are adverse to commercial prosperity ; yet the 
effect may happen to be counteracted by other circumstances. 
The United States of America, in the abundance of land to be 
occupied, can prosper under many arrangements that would be 
ruinous to Great Britain. 

The other Experimental Methods. 

29. The Method of Difference may be exemplified in 
Political Cause and Effect. 

The introduction or withdrawal of a single agent, followed at 
once by a definite change in other respects, is our most cogent, 
as well as our shortest proof of causation. In the complications 
of Political Society, we cannot always be sure that- only the 
one innovating circumstance is present ; so many unseen ' 
operations being always at work. This source of ambiguity is 
practically overcome when an agent suddenly introduced, is 
almost instantaneously followed by some other change ; as when 
the announcement of a diplomatic rupture between two nations 
is followed the same day with a derangement of the money 
market. 

According as the supposed change is more gradual in its 
introduction, and the consequences slower in their develop- 
ment, the instance is less and less a decisive example of differ- 
ence. The deterioration of value is saved only when we are 
sure that every other thing has remained the same. A new 
religion introduced into a nation, remarkably stationary in its 
other institutions, would be held as the cause of all the subse- 
quent changes. 

30. Agreement in Absence may be advantageously re- 
sorted to in Politics. 

We compare the cases of the presence of Poor Laws, of 
Commercial Restrictions, of a Standing Army, of Local Self- 
Government, — with the cases of the absence of these institu- 
tions ; and if any circumstances uniformly present in the one 
are uniformly absent in the other, the force of proof is greatly 
augmented. 



30. Concomitant Variations is employed in 
political causation. 

There is a marked concomitance, in the History of \ 
between the growth of Free Institutions, and the pr, 
the nation, both materially and intellectually. Tin 
compared with the inverse instances of Greece and B 
where, by a gradual process, the extinction of liberty was 
ultimately followed by intellectual and social dec.,. 
all these instances, in the complications of Politics, may not 
be final ; yet they afford a very high presumption of ca 
effect 

The Deductive Method. 

31. The Deductive Method, in conjunction with the 
Inductive or Experimental Methods, must be regarded 
the mainstay of political investigation. 

Neither the Deductive Method alone, nor the Inductive 
Methods alone, can be trusted in the complications of the 
social science. Their mutual consilience or confirmation, ig 
requisite in order yield trustworthy conclusions. 

Pure Deduction appears to most advantage in following out 
the tendencies of separate agents. This is the motive for 
subdividing the Social Science into branches, as Political 
Economy, &c. The tendency of the single motive of the 
desire of wealth can be studied apart from other tendencies. 

An essential part of political deduction consists in tracing 
the wide operation of the Sentiment of Power, in the va: 
degrees of its development among human beings, and under 
all circumstances. The deduction should comprise a wider 
area than mere political situations. 

The Sociability of mankind, their Sympathies, the grades of 
Intelligence, have consequences traceable by a purely deduc- 
tive operation. 

We might even venture a certain way in the second deduc- 
tive process — Calculation or computation of concurring agen- 
cies ; as Wealth, Power, Sociability, Sympathy, with Hal 
Customs, &c. Here, however, we become aware of the help- 
lessness of the deductive method by itself. Havii 
quantitative estimate of the separate agents, oni pi to 

combine them in a quantitative sum, is entirely h< 
errors of calculation may be so wide as radically I the 

conclusions. 

It is the third step of Deduction— Verification— that givui 

25 



568 LOGIC OF POLITICS. 

the method all its weight, by joining it with Inductions. In 
point of fact, politicians in applying the conjoint methods 
usually have an inductive or empirical generality presented in 
the first instance ; which induction they compare with the 
deduced tendencies of the agents concerned. Thus the work- 
ing of despotism is first given as an empirical generalization 
from history ; we then compare these alleged results with the 
deductive consequences of the love of power, and all other 
human motives, both of the ruler and the ruled, entering into 
the situation. Such maxims as the following require, for 
their verification, the consilience of induction and deduction. — 
1 The possessors of supreme power, whether One, Few, or 
Many, have no need of the arms of reason ; they can make 1 
will prevail.' ' The governments most distinguished for 
sustained vigour and ability have generally been aristocracies/ 
The deductive reasons in favour of this last position are 
founded on the consequences of devoting a small number of 
men exclusively to public business. 

Thus, the usual course of the Deductive Method is to lay 
hold of a number of empiricisms, derived from history and 
political experience, and to subject them to the test of deduction, 
thereby converting them into derivative laws. Considered as 
inductive generalities, everything should be done for them ' 
that can be done by strict compliance with the Inductive 
Methods ; after which they are to come into comparison with 
the deductive results of the tendencies concerned. 

Among Empiricisms demanding to be confronted with 
deductive conclusions, we may instance the following — ' modern 
civilization tends to collective mediocrity,' (J. S. Mill) ; 4 unity 
in religion is unfavourable to civil interests ' (Gr. C. Lewis) ; ' 
1 there is no necessary connexion between hereditary royalty 
and hereditary nobility ' (ib) ; ' the human race is on the 
whole progressive ' ; ' there is a constant relation between the 
state of society and the state of intellectual speculation ' — 
(Comte). 

Deductive confirmation is especially needed in assigning the 
causes of some one historical event. Unless there happen to 
be other events closely analogous, our inductive basis is of the 
slenderest kind ; succession may be taken for causation with- 
out any check. Thus, the account of the rise of free institu- 
tions, in modern Europe, must be far more deductive than 
inductive. 

The introduction of Christianity into Europe co-existed with 
bo many other changes, that its consequences cannot easily be 



EMPIRICAL AND DKKIVA 

eliminated. Our only means of varyii 
take the separate nations apart ; but in none 
one cause "introduced singly. lion 
political and other results of Christian] 
deductive confirmation; and we find thai 
largely appealed to. The tendencies of the I 
are laid out deductively, and the attempt is made 
coincidence with the facts. To be properly c 
deduction should be made of all other tendencies- 
Roman influences, and the mental endowments of tin- I 
races ; which subtracted from the total would give 
the Method of Residues. 

In the foregoing brief allusion to the Deductive M 
included a reference both to Empirical and to Derivative L 
The subject of Politics furnishes pertinent example 
limitation of Empirical Laws, and in a less degree of D 
Laws, to adjacent cases. There is safety in extending an 
pirical law only to the same territory, the same time, 
similar circumstances. When a ten pound suffrage had 
sisted in Britain for thirty years, with good effects, it v 
small matter to risk the extension to a seven pound or 
pound franchise, on the mere faith of the empirical eon 
whereas, the sudden transition to universal suffrage, could 
be relied on from the same empiricism. The conseqnenc 
such a step, if computable at all, could be computed onl 
the aid of deductive reasoning — by the establishment i 
vative law. A well-informed, sagacious, and unbia* 
might be trusted to predict, within certain limits of I 
probable issue of such an extension of the fra 
by a superior handling of the deductive method. 

The Method of Residues being properly a Deduc 
is occasionally valuable. It takes the problem on 
aspect; as in the case of Christianity already 

In applying the methods of Agreement and of ; 
single out a cause, our prior knowledge of tb 
of the cause, prepares us to receive the in 
without the misgivings that we must feel wh 
nothing on this head. 

Hypotheses in I 

32. In Politics, we are seldom im 
assuming an unknown agency ; the known 
nature are the sufficing causes. Our 



J o 



570 LOGIC OF POLITICS. 

the presence, and the amount, of the supposed agent ; and 
these may be proved by their exactly tallying with the 
facts. 

Assumptions are perpetually made regarding the conduct 
of human beings under all circumstances. The passions of 
Power, Pride, Fear, the Self-interest of men, their Sympathies, 
are all real or genuine causes. There may be doubts which of 
them produced a certain line of conduct : and we may apply the 
logical conditions of hypotheses to solve the doubt. If any one's 
actions tally precisely with the consequences of Love of Power, 
we receive this coincidence as so far a proof of the hypothesis. 
But the proof is completed only by showing that the action 
does not tally with any other motive; a thing that we cannot 
always be certain of. The execution of Charles I. might have 
resulted from the fears of the Puritans, from their revenge, 
from their ideas of justice, from their interpretation of the 
designs of providence. A proof from hypothesis would have 
to show that the act coincided fully with the tendencies of only 
one of all the supposable motives. 

Simplification of the Political Problem. 

33. There are various modes of reducing the complica- 
tions of Politics. Several of these have already been 
glanced at. 

(1) By studying Institutions separately, due regard being 
had to their mutual action. This is that primary Analysis of 
Society which is the groundwork of scientific method through- 
out. There may be difficulty in making the isolation, and yet 
allowing for mutual influence ; but any other method is 
hopeless. 

(2) In modern political theory, much stress is laid upon 
the distinction between Order and Progress ; and we are 
recommended to study separately the influences tending to 
Order or Stability, and the influences tending to Progress or 
Improvement. The advantage of this separation is chiefly to 
divide the field of study, for the ease of the understanding. 
It has been shown by Mr. J. S. Mill (Representative Govern- 
ment, Chap. II.) that the two interests cannot be absolutely 
separated ; there can neither be Progress without Stability, 
nor Stability without Progress ; yet the problem of Society is 
greatly simplified by first studying each by itself, and then 
paying attention to their reciprocal action. 



SIMPLIFYING OF POLITICS. 

Mr. Mill has traced, by the combined Inductivi 
tive Methods, the conditions of Stability in 
has referred them to the following heads : — | 
the citizens calculated to imparl . 
(2) a feeling of allegiance or lovn 
element of cohesion among the members 
is apparent that all these causes, while 
inductive comparison of societies, may also be I 
from general principles of the human mind ; 
the two results being essential to the pi 

(3) In the variation of political circumstai 
tions of society would be numerous beyond en 
for the eminently scientific device of einbodj 
number in their exact circumstances and c 
they may be varied at pleasure. It: may be a que 
certain public works should be overtaken by the 
government or by the local government ; . 
prisons, &c. Now the decision of this question in 
case, if accompanied with all the circumstantials thai 
the decision, is the decision for innumerable o:i 
although differing considerably from one anotl 

i the central government undertakes the work, avow 
solely because the locality cannot bear the expense, this 
also the opposite case, where the locality 

It is thus that legal judgments, if accompanied with a 
statement of reasons, may apply to a wide i 
cases. And so also with all reasoned conclusions h 
The very same proposition that declares the cons 
despotism in given circumstances, impli 
consequences in degree, as the despotism 
and the reversal of the consequences by tl 
freedom. All such adaptations and principles are to be held 
as of the nature of deductions, for which induct i. 
is desirable according to the extent of departure from 
embodied. 

(4) Attention has already been call- 
that Politics deals with men coiled 

In the view of the politician, a million of hum! 

less complicated thing than a single ii 

scale of the operation reduces its compl 

for governing a nation (in a certain rode 

than the maxTms for man: 

consider all the minute peculiarity 

Minister, who has to transact business with one individual, 



572 LOGIC OF POLITICS. 

may have his ingenuity and patience more severely taxed than 
the Home Minister, who deals with the mass of a nation. 
The limits of the proposition are contained in the reasons of it 
(as just remarked) ; if the mass of the community breaks up 
into individualities, by social discord, there is an end to the 
facility arising from collectiveness of action. 

(5) Not the least important simplification of the Political 
Problem, whether for theory or for practice, is the Limitation 
of the Province of Government — the transferring of business 
from Public to Private management. The tendency of all 
societies has been to Over-government ; and the relaxation of 
this is one of the favourable symptoms of existing societies. 
The proper province of government is a question to be solved 
according to the circumstances of the time. A state religion 
may be suitable under one state of things and unsuitable in 
another ; so great are the advantages of disburdening the civil 
ruler of such a charge that a case must always be made for 
retaining: it. 

Fallacious Methods in Politics. 

34. These are for the most part implicated in the state- 
meat of the sound methods. 

(1) The exclusive employment of the Experimental Methods is 
shown to be insufficient in the complications of Politics. How 
much more so is mere Agreement without the studied variation 
of circumstances demanded by the method; and yet such is 
the usual procedure of untutored minds. Thus, any institution 
whatever is pronounced beneficial, because the country has 
prospered under it. This is the grossest form of empiricism. 
The careful employment of the Experimental Methods would 
avoid such errors ; but would still be inadequate. 

(2) A purely Deductive Politics is equally at fault. Even 
starting from the best Psychology, and the best Ethology elabo- 
rated with an express eye to Politics, we should never be able 
to infer tendencies with perfect precision, still less to compute 
the sum of a plurality of tendencies. With the highest skill 
in psychology, with the best possible appreciation of the ave- 
rage development of the great leading attributes of the mind, 
in a given race of men, and with the closest attention to 
physical and other circumstances, — we should still break down 
in the attempt to say, how a community formed from such a 
race, could prosper under either a despotic or a democratic 
government, with or without a religious belief. 



I 



TUE POLITICAL LND. 



Allusion Las been made to the en 
cause in a single circumstance, ins! 
tion, or group of circumstances. 

(o). Sir G. C. Lewis has fully illn 
false and fictitious causes iu Politics, Such 
legendary causes; fictions of law ; and the 
contract suggested by Grotius, and formally argued bj 

PRACTICAL rOLI 3 

35. In every Practical Science, we must begin bj 
forth the End. In Politics, as in Ethi 
variously viewed. 

In most practical sciences, there is no dispute as to the • 
In Ethics, and in Politics, the case is different. 
parties agree to call the end * human happiness,' they 
the meaning attached to it. 

In antiquity, the Athenian and the Spartan 1 
ciety were totally different ; so much so that, on the basis o! 
same Theoretical Principles of Society, the rules of I 
would be distinct. The end in the Roman Republic was the 
power and glorification of the State. A leading design ol 
Spanish rule of America was the conversion of the nations to 
Catholicism. 

According to some, the end of the political machine 
government, or the best mode*of carrying out the | 
objects of Defence, Security, &c, on whose account so 
exists. If a despotism accomplishes this best, a des] 
the best government ; if not, not. 

Others, as Mr. Mill, maintain that the cultivating of the 
energies of the people is an end independently valuable 
this is coupled with the farther assertion, that by such mi 
alone can a high standard of government be maintaii 
both parties agree as to the end, but differ as to the* I 
It is, however, possible to maintain that a wor 
the people themselves, is preferable to a better ti 
them. 

Another way of expressing the same antitli 
contrast passive enjoyment with free action. 1: I 
on the one side, that what gives I 
pleasure with the least pain, is the higl 
and, on the other, that what allows thegr 
and individuality, with or without m 
absolutely the best. 



574 LOGIC OF POLITICS. 

These different modes of conceiving the ends of society have 
a great influence on actual practice. The ' paternal govern- 
ments ' will not conform to the plan of leaving to the individual 
the utmost liberty compatible with the liberty of others. 

36. The Political end being stated, the principles of 
Theoretical Politics are all convertible into maxims of 
Practice. 

The principles of Causation in society, when stated as laws 
of the order or succession of events, are theoretical principles ; 
when stated as rules for effecting a given object, are practical ' 
principles or maxims. Discussing theoretically the work- 
ings of Democracy, we trace certain tendencies of the predo- 
minance of the numerical majority, and the tendencies of 
certain political arrangements to counteract these ; whereupon, 
having in view the end of allowing no class unlimited ascend- 
ency, we lay down as a maxim or rule the providing of such 
checks. 

Theoretical politics enounces the proposition that certainty 
of punishment is more deterring than severity ; practical 
politics converts this into the precept, — Make punishments 
certain rather than severe. 

The requisites of Stability above laid down are convertible 
into maxims for attaining stability. So with the theoretical 
conditions of Progress. 

Although Practical Politic* is thus Theoretical Politics 
over again, with the addition of well defined ends, there are 
great advantages in laying out the subject in both forms, we 
being aware that the substance is the same. The theoretical 
form is the one most convenient for investigation ; while the 
repetition of the principles in the preceptive dress, if done so 
as not to confuse the mind, is both suggestive and corrective. 
Moreover, it is only by the separate treatment of the two 
departments, that we do full justice to the special point raised 
in the practical department — the political end. The full 
handling of the various modes of viewing the end would 
justify a long preliminary chapter of Practical Politics. 

It has been well pointed out by Sir G. C. Lewis that the 
propositions of politics are ordinarily cast at random, some- 
times in the theoretical, sometimes in the practical mould. 
4 The more haste, the worse speed ' is theoretical ; 'festina, 
lente,' is practical. 

Much of Theoretical Politics may be unavailing for practice, 
at least the limited practice of a given country and time. The 



PRACTICAL DEVICES IN roi.n 

theory of Politics, in its most imposing • 
bends the Philosophy of Universal History, muc 
of limited practical application. Hence the p uctic 
is content with selecting a portion "1 what lia 
in theory. 

Again, the practical mode of selection has the fart! 
liarity of altering the arrangement or grouping of the 
dicta. In the theoretical investigation, the- ; 
different institutions are described in an 
Forms of Government, War organization, Police, Jo 
With a view to a practical end, we borrow from mai 
ent parts of the theoretical exposition, 1 1 
and effect conjoined in a peculiar structure, as for example, 
Poor Law of a given country. This is the prevailing Ibrm «>f 
all practical departments with reference to the allied 
cal sciences. 

Many of the greatest social devices have 4 
sively in the hands of men of practice, and have been s § 
first in the practical shape ; being afterwi 
theoretical propositions. Such are the English Com 
the union of Local Management with Central 
Inspection, the system of fastening Responsibility upon 
real authors of political acts. Mr. Mill regards as one of the 
most valuable securities yet devised for good gorerni 
device that grew up in the East India Company's rule, oai 
to associate the chief administrator with a Council I 
but not to compel; thus leaving the J upon a 

definite individual. 



CHAPTER IX. 
LOGIC OF MEDIC1XE. 

1. The scope of the I 
given by the Definition of the correl; 
and Disease. 

The phenomenon, expressed by Health on oi 
Disease on the obverse, is indefi 
human experience like Life itself, of which i1 
or manifestation. The attempt to , 
to a person that had never Been or 



576 LOGIC OF MEDICINE. 

of disease, would entirely fail. To call it * a perverted Life 
Process ' is to give an analogical phrase, but as the phenome- 
non is unique, analogy gives no assistance. 

Thus, although Disease is a highly complex fact, yet so 
novel are its manifestations, that we must define it by the 
methods adopted for our simplest experiences, as resistance, 
motion, colour, line, angle. "We must refer to a number of 
examples in the concrete, and generalize these into a com- 
prehensive statement, which the examples make intelligible. 
After we become acquainted with a certain number of diseases, 
the others can be understood by description alone. 

It is barely possible that without actual experience of In- ; 
flammation, one might form a constructive notion of it from 
its technical characters — objective and subjective. The objec- 
tive characters — redness, swelling, heat — might be conceived ; 
the pain also, if otherwise known to us, could be called to 
view, and united with the other symptoms ; and the mind 
might laboriously fuse the whole together. This is only not 
impossible. But the greatest powers of description in the 
expositor, combined with the highest constructive faculty in 
the learner, would break down in the endeavour to realize 
Fever. The subjective experience, being one unknown to a 
person that had never been out of health, would be unintelli- 
gible in the- reference. 

A few experiences of Disease give a meaning to the corre- 
lative notion — Health ; whence we can define disease negatively, 
by the infringement of Health. The positive definition, would 
be the result of the comparison of all the modes of derange- 
ment, the generalization of diseases ; but writers usually 
remain content at the outset with the negative statement ; in 
other words, they define Health, by assuming the knowledge 
of a few specimens of disease. Health, in its most complete 
acceptation up to this time is the absence of all the 1146 dis- 
eases put down in the 'Nomenclature of Disease,' 

The science bf Medicine is an adequate description of all 
these forms of derangement, or departure from Health, with 
a view to suggest means for averting or removing them. This 
practical end implies an extensive knowledge of causation with 
reference to Disease. 

As regards the large number of Diseases, the complicacy of 
their characteristics, and the existence of generic and specific 
agreements and differences among them, impart to the science 
of Medicine a certain community with the Natural History, 
or classificatory sciences — as Mineralogy, Botany and Zoology. 



BIOLOGY iS TIIE BASIS OF MBDH 

The analogy to the two last is still 

stance oi evolution, or the succession of si 

eases. 

Sciences preparatory 

2. Disease being a state of the Human system, th 

of medicine rests immediately on the part of Biolo 
Human Anatomy and Physiology. 

All animals, and even plants, are liable to abnonna 
or disease. The consideration of the subject, ho* 
the highest development in connection with hi 
Animals share in many of the human d. 
special to themselves. 

When we name Biology, we may be supposi 
the sciences preparatory to medicine. Stric 
is true ; inasmuch as all other knowledge applica 
is applicable through biological science. Yet it is welJ 
emphatically to the inorganic sciences— Natural Phi 
and Chemistry — which, in their present improv 
yield many suggestions bearing at once on the 
Physics, in both its divisions — molar and molecular, Chemi 
— both Inorganic and Organic, are full of applicaj 
medical biology. The medical man, in order to derive th< 
benefit of these scienes, needs to study them apa 
in their applications in Human Physiology. 

Intermediate between Human Physiology and the I 
of Physic, are the exhaustive enquiries into m 
and special functions ; as exemplified in the work i 
on Urine, and in the researches of Dr. Edward Smith, J 
Haughton, and others, as to Food, Muscular Power, i 
tion, and other applications of Physics and Cbejniai 
experimental checks and verifications. 

Pathological, lasccl on Physio ' 

3. The Analysis of the Orgai 
purposes is likely to prove a basis of Path' 

It being found that the greater number 
localized in separate organs or tissm 
ing diseases, by a lull enumeration of all those in 
diseasable parts. Now, Physiology ftp the lepai 

tissues and organs of the body; 

whether these are all separately sub sease. 'i 

classification of diseases (Aviih the exception of what are 



578 LOGIC OF MEDICINE. 

termed general diseases) is made to follow the physiological 
division of the organs — Brain and Nervous System, Senses, 
Circulation, Absorbent System, Ductless Glands, Respiratory 
System, Digestive System, Urinary System, Generative 
System, Organs of Locomotion, Cellular Tissue, Skin. And 
inasmuch as most of these systems are complicated groups of 
organs, for example, the Digestive System, a farther sub- 
division is made of localities of disease — as Teeth, Gums, 
Tongue, Salivary Glands, Stomach, Intestines, Liver, &c. 

This Anatomical arrangement of the seats of disease would 
be of little value, did not diseases confine themselves to 
separate organs, while exercising a secondary influence on 
adjoining and connected parts, or on the general system. 
Thus, a disease may accomplish its entire course in the 
bronchia, the stomach, or the kidney, with- no farther injury 
to the rest of the system than arises from disturbing the 
balance. When one member of a business establishment is 
incapacitated, a certain deranging effect is felt throughout the 
whole ; but that effect is a different thing from the incapacity 
of one making the incapacity of another. 

The point for the pathologist to consider, therefore, is 
what parts and tissues may be saparately diseased. This is 
to push the local analysis of disease to the very utmost. Each 
of the parts, thus distinguished, must be supposed to have 
independent vigour or weakness, as measured by the energy 
of function, and by the resistance to deranging causes. 

Even in properly local diseases, however, there must be 
more or less tendency to affect adjoining or connected organs ; 
and there is thus a scale of kindred established between each 
organ and the rest ; disease of the stomach affects the intestines 
and the liver before the lungs or the kidney. 

It must be admitted, however, that the alliance of local con- 
nexion is apt to be overborne by the distant alliances established 
through the two carrying organs — the blood and the nerves. 

4. The analysis of physiological Functions is also an ana- 
lysis of diseased actions. 

Every function performed by an organ may be affected in 
disease ; and, in some cases, one function may fall into disorder 
independent of the others. Thus the liver has a plurality of 
functions ; and disease may consist in changing one, with no 
more than an indirect result upon the rest.- The pathologist 
needs to avail himself of this analysis likewise. 



GENERAL PROCESSES IN I 

5. A farther analysis must bo made of morbid Pi 

!or substances generated in disease, and 
same localities during health. 
This is a department special to morbid Anaton 
logy; and is prosecuted by the assistance of chemical 
and microscopical examination. All such produ 
carefully ascertained, classified, and described. A 
account of the characters of each, some mention mighl 
made of the diseases wherein they severally manifi 
selves. Finally, their causes, known or supposed, i 
given. But care is to be taken not to jumble up all tl 
three expositions in one. 

There is a close and natural connexion between the 
of new morbid deposits- and the morbid alterations of the 
several tissues. The same method needs to be followed with 
these; each morbidly transformed structure being described 
with reference to all its appearances and re-actions, ascertained 
by chemical, microscopical, or other means ; the descriptioi 
be followed as before by mentioning the diseases wherein each 
occurs, together with any assignable causes of the chai 

Enumeration of Diseased Processes — General Pathology. 

6. The numerous diseases affecting the various organ 
the body, as well as those attacking the whole, coi 

the repetition of a small number of diseased pr< Such 

are Inflamation, Congestion, Haemorrhage, J < 
Tumours, &c. 

7. The process called ( Fever' is consid< 
disease. 

Upwards of twenty forms of diseased process can be 
rated ; Fever and Inflammation taking the lead. This 
less a great means of simplifying disease, although, in the 
specific varieties of the different processes, there i 
able burden of detail. Inflammation is pretty m 
in all organs; being similarly caused, and similarly broi 
to a termination. 

It is proper to give a general and comparative 
every one of these processes, adverting to their m< 
varieties, before taking up the special diseases wL 
enter. Chapters on Fever in general, and on Inflame 
general, are usually provided in advance of the detailed 
scription of diseases. 



580 LOGIC OF MEDICINE. 



General Therapeutics. 

8. The generalizing of Diseases, through the recurrence 
of a limited number of diseased process, suggests the 
generalizing of Remedial agencies. 

13 y way of anticipating the remedies for the special diseases, : 
there is the same propriety in taking a general view of 
remedial agencies, as in taking a general view of diseased 
processes ; the one being made possible by the other. Very i 
great advantage accrues from studying each remedial agent, j 
not apart from all particulars, which would be absurd, if it were i 
possible, but in connexion with all particulars. 

For example, that remarkable fact called by the various ; 
names — metastasis, counter-irritation, derivation, revulsion — A 
should be discussed at the outset on a comparative survey of 
its characters in all variety of circumstances. This is the 1 
only means of gaining a clear and steady grasp of its compass 1 
and limitations, or of the causative conditions of its working. 

Again, a similar generalized view should be taken of the 
process called Stimulation, whereby, through a variety of 
means, nervous action is heightened, with an increase of other i 
dependent functions. 

The justification of a General Therapeutics, to assist both 1 
in investigating disease, and in treasuring up knowledge for 
use, is apparent in the great number of diseases that have no \ 
specific. Take Typhus, for example. The only directions 
given relate to the employment of the general remedies 
adapted to the symptoms of the disease ; cold affusion or 
cooling drinks for the main fact — excessive heat ; stimulants 
to resist the depression of the powers ; purgatives when the 
bowels are confined ; sudorihes, &c. 

Although the removal of the cause of a disease, with the I 
occasional plying of the opposite, must always be a large part 
of Therapeulics, it does not make the whole. When the 
poison of typhus has once entered the blood, the removal of 
the cause is irrelevant ; the effects are already produced, and 
must be counteracted by new agencies. Hence, we have first, 
General Causes of Diseases, with Hygiene (which a know- 
ledge of causes may fairly exhaust) ; secondly, General Thera- 
peutics, as counterworking the derangement actually produced, j 

General Therapeutics might thus conveniently follow the 
general account of the Causes of Disease. The two branches are 
closely connected without being identical. The general causes 



DEFINITIONS OF 55 j 

t are such as— Hereditary Constitution ; 

(Miasmata, Cold, Heat, Light, 

able Food and Drink ; Over-exertion or I. 

Sleep ; insufficient Exercise ; Poisoi 

6f these noxious agents is implicated the bran 

or warding off diseases by avoiding their ca 

are indicated, obversely, the cau 

which we measure by the distance plac 

ease. 

The Materia Medico, usually contains ;i Thcrap 

fication of Medicines; as Tonics, Exhilaraui 

Emetics, Purgatives, Sudorifies, Diuretic.-, 

detail of properties under each of thesi 

the larger works on Materia Medica, is to a g\ 
\ repetition of general Therapeutics. 

Notions of Medicine. — Definition and ( 

Diseases. 
9. Of Disease on the whole, there is no <1 
is of any value ; defining begins with the special ap] 
ances of disease. 

The very best generalization that can be given < 
t'ie whole, is too vague to furnish any useful in 
When we begin to specify morbid appearances, a ff tho 

name of a Disease, to group those that are com 
same outbreak, we are enabled to construct definiti 
short of absolute precision, yet faithful to 
actual instances. 

The Notions of disease concern (1) d : 
1 (2) diseases. The diseased processes inclu 
r mation, Congestion, Haemorrhage, Dro 
• trophy, Degeneration, Tumours, Par 
i weakness, &c. Of these vario 

distinguished for their prevalence in common di8< 
, Inflammation, Degeneration, and Functional de 

Fever.— Fever ix a general state ei itomany 1 

and now susceptible of being chara 
acter. Mainly through the "careful 
a generalization of Fever has been arri 
ciliate all the ap] 
by the simple fact—' Elevation of 
temperature in the body generally, to th 
Fahrenheit, is a state of Fever; while the increase 
ceed to 6°, 8°, or even 12° Fahren! 



582 LOGIC OF MEDICINE. 

As there is no circumstance characteristic of Fever ir 
general, but this one fact, and its implications or consequences 
this is the complete definition of the febrile state. Any expla- 
nation or illustration of it should consist in stating a variety 
of instances showing the elevated temperature. 

The following definition is encumbered with statements not 
belonging to the definition — ' A complex morbid state accom- 
panying many diseases as part of their phenomena, more or 
less constantly and regularly, but variously modified b} 7 " the 
specific nature of the diseases which it accompanies. It 

ESSENTIALLY CONSISTS IN ELEVATION OF TEMPERATURE, luhich must 

arise from an increased tissue change, and have its immediate 
cause in alteration of the nervous system.' The first sentence is 
a pure superfluity. The setting apart of Fever for separate 
consideration, as a preliminary to the discussion of particular 
febrile diseases, implies what is therein stated — that fever is a 
morbid state, and that it accompanies many diseases. All 
such wordiness should be sedulously avoided in definitions. 
A different criticism applies to the expressions given in italics 
— ' arising from an increased tissue change,' ' having its imme- 
diate cause in alteration of the nervous sj-stem.' These are 
not idle phrases, but describe circumstances of radical import- \ 
ance. Why, then exclude them from the definition ? The 
reason is that the complications of disease require the separate 
discussion of whatever can be separately discussed w r ith ad- 
vantage ; and, almost everywhere in medicine, it is advan- 
tageous to separate the description of 'the fact, from the 
enquiry into the causes of the fact. A definition should give 
whatever is essential to the determining of a fact or pheno- 
menon. It should not assign the causes, nor deduce the 
consequences of the phenomenon ; this is to advance beyond 
definition to predication, and should be a distinct expository 
statement. 

It is a proper appendage to the definition, to enumerate the 
ordinary superficial appearances of fever, which constituted 
its definition before the exact generalization w T as arrived at, 
' hot skin, quick pulse, intense thirst, scanty and high-coloured 
urine ;' at the same time subjecting these symptoms to a critical 
examination, so as to point out their shortcomings. 

The fact of Elevated Temperature being sufficiently shown 
by an appropriate selection of particular cases, the important 
predications above alluded to may be taken up. From the 
Law of Conservation, as applied to the animal economy, there 
must be an increase of tissue change to support the heat, and 



DEFINITION OF FEVER. 

ihe endeavour should be made to assign thi 
its exact circumstances, and numerous outlying 
> account of fever is not complete without 
i The conclusions of Dr. Parkes, obtained by a large indui 

and corroborated deductively by the Law ol 
$ most valuable. 'The increase of tern perntnro maj 
I frequently) attended with increased elimination ; 
i presumably with increased tissue change, a, what I 

I to contradict the general law of Conservation"— ' the pro I 
{ of metamorphosis, as judged by the excreta, may 
; in febrile cases.' The contradiction, however, is only 
' for there is good evidence in such cases, of an nndoe 
of excreta, which makes one of the bad accompaniment 
fever. Careful observations prove that while thi 
J amount of excreta is small, the tissue-change may still he - 
It is obvious that this topic involves a •_ 
detail, ascertainable only by observation, although check* 
the general law of definite changes accompanying definite 
results. The state of every organ, and tho alteratii 
the excretions — pulmonary, urinary, cutaneous, ii 
&c. — need to be exactly gathered from the facts, and ma 
clue to the windings of the special febrile disease. 

The second predicate given with the foregoing definition — 
'the alterations in the nervous system ' — also deserves to be 
illustrated, proved and unfolded, in a separate section. 

Other important predications extend the Hi^ 
such are the procuring cause, and the course or o, in 

so far as belonging to fever generally. 

The foregoing outline represents the exhaustive account of 
Fever, as a diseased process. "We bc^an with the int 
illustrating definition in Medicine ; but, it was ;, 
for all, to show the boundary between legitimate definition and 
predication, which is habitually disregarded in medical sub- 
jects to the detriment of the handling, both in a logical p 
of view, and as regards expository clearness. The filling 
up of the sketch would be the account of Fever, 
a previous heading — Enumeration of I 
(§6.) 

Inflammation. The complication of 
able*; but the method is plain. AY tho 

definition from the predications; and, in the definition, wo 
may separate the superficial appi 
diagnosis, from the essential fact, or facts of the state. 
First as to the definition. The traditional characters of inflam- 



5S4: LOGIC OF MEDICINE. 

matiou are the four facts — redness, swelling, heat, pain — whicl 
are a tolerably close approximation. There might be a con- 
venience in briefly illustrating these points, as a prelude to the 
improved generalization that can now be afforded. 

Even then, however, the only correct course is to adhere 
in the first instance to a description of the characters, for the 
purposes of identification ; refraining from all remarks bearing 
on the causes or explanation of the several symptoms. The 
kind of redness, its various hues, the more or less extensive 
prevalence of the mark, — are the points proper to the eluci- 
dation of the property as a defining and diagnostic circum- 
stance ; the same rigid plan to be followed with the three 
remaining symptoms. The triumph of the expositor's art 
in this effort would be, that no one could ever mistake the 
inflammatory redness, swelling, or the rest. 

The appearances being thus expounded with all the neces- 
sary enforcement, it is admissible to consider how far they 
may be connected, either by implication, or as cause and effect, 
with one another, or with circumstances still more funda- 
mental. It is then easy to point out that the fact of congestion 
is a very important addition to our knowledge, and, if imparted 
on the plan now stated, re-acts on our previously obtained 
knowledge, by resuming in a single statement all the four facts, 
and still more, by accounting for the failures of one or other 
of these in particular instances. 

The faulty mixing up of description with causation is exempli- 
fied in the following sentences regarding Inflammation : — ' Yery 
often the pain is a "bulking" or throbbing pain — every beat of 
the heart makes itself felt in the tender part. The pain of inflam- 
mation results no doubt, from the implication of the nerves in the dis- 
eased processes.' ' Speaking generally, therefore, there is more pain 
felt in external inflammation, because there are more nerves of com- 
mon sensation.' 

It is next to be seen what better account can be given of 
inflammation, grounded on the superior physiology and ob- 
servations of recent times. The definition of Dr. Aitken* is 

* A complex morbid process characterized, — (1.) By a suspension of the 
concurrent exercise of function among the minute elements of the tissue 
involved ; (2.) By stagnation of the blood and abnormal adhesiveness of 
the blood aises in the capillary vessels contiguous to the tissue-elements 
whose functions are suspended; (3.) By contraction of the minute arteries 
loading to the capillaries of the affected part, with subsequent dilatation 
and paralysis of the contractile tissue of the affected blood-vessels. The 
nutritive changes between the blood and the minute component elements 
of the affected tissue become visibly altered, and although an appreciable 
exudation does not necessarily follow, yet a constant tendency betrays 



I 

DEFINITION OF INFLAMM 

rery exhaustive, but might be disburdened i 
nore suitable to predication. The following apj 
iitials of the enumeration. 
(1) Suspended function of (he //> 
| irom the observations, that an alteration oi 
is to impair iis proper functions, that is, il 
olood in the way of absorbing nourishment, and 
or other functions— -is the primary fact, the 
the subsequent changes. 
I (2). Stagnation of the Mood. 
J (o). Abnormal adhesiveness of the lien 
'adjoining. 

(4). Contraction of the minute arteries supplying t 

iof the part, folloiced by dilatation and loss of contractu 
(5). A tendency to exudation, varying according to 
I stances. 

Kot until each of these constituent facts is made intellig 
and verified by references to observation, should a 
be commenced as to their causative connexions i bem- 

selves, or with other facts. The description being 
dered complete and intelligible, there is the great< 
trying to show, for example, that the first fact— sue 
tion of tissue — leads to the blood derangement* 
enumerated; and that the heat, redness, swelling, and pain, in 
the old enumeration, follow as effects from the trai 
cumstances, as given in the definition. 

The new growths and deposits should be reserved 
tinct predication. So also should be the cause i 
attack, whether favourable or unfavourable. 

The extreme variations of degree inmorl i 
appearances scarcely short of differeocea of kind; ; 
have to be explicitly enumerated, as specific modi 
phenomenon. A distinct consideration should 
such an important accompaniment as !'■ 

itself to the occurrence of an interstitial exudation, 1 

proper regimen and proper r(m< dire, is often aboith 

tion follows as a result of tin; ii 

with an unhealthy condition of the Mood, mid of tl 

to he associated with vaiied forms of m 

The elementary structure in winch il occurs; (2.) 

conditional or local disea.se with w) ich tl 

may co-exist ; and (3.) Aecoi 

the amount and suddenness of the <•:' 

the diminished vascularity, and the \ 

ing parts.' 



5SG LOGIC OF MEDICINE. 

ditions of it (the chief being probably severity of the loca, 
attack, and poisonous virulence). ^ 

The hypothetical views started, in the absence of a theory, 
to connect the whole cycle of circumstances should be given 
last of all. 

To frame definitions of Degeneration and Functional Disease, 
beyond the statement of the palpable appearances so named,, 
would involve hypothetical considerations, such as require to 
be admitted into medicine, with due regard to their exact \ 
value. 

Correlative with the definitions of Health and Disease 
generally, are those of the important words Constitution, Tem- 
perament, Diathesis, indicating a hypothetical permanent con- 
dition of the system, manifested by the tendency to incur or to 
resist diseases ; and more especially diseases of enfeeblement 
and degeneration. A weak chest, a strong stomach, suscep- 
tible nerves, — are modes of stating in a useful form such actual 
occurrences, as that certain persons are easily affected with 
chest disease, or resist the agencies of stomachic disorder, and 
so on. They suggest the mode of life best fitted in each case 
to ward off attacks of disease. 

Definition of specific Diseases. — The very general states 
above quoted exemplify definition under the greatest simplicity, 
as respects the number of characters, although not as respects 
the generalizing and seizing of the true characters. When 
we proceed to the more concrete forms of disease, Typhus, 
Gout, Pleurisy, Neuralgia, Jaundice, &c.,we have the general 
processes, Fever and the rest, with many various accessories, 
constituting the specific characters of the individual affections. 
Consequently, the definitions are apt to be voluminous in their 
statement ; and there is still more need of method. 

Examples have now been given of the two different modes of 
medical definition ; the one corresponding to Diagnosis, and 
framed with a view to identify a disease by such signs as are 
best accessible ; the other, the most complete generalization of 
the essential fact or facts of the disease, which facts may or 
may not lie upon the surface. The first is requisite for 
distinguishing diseases ; the second, for understanding them. 

Let us take an example. Gout is defined by Dr. Garrod — 
i A specific form of articular inflammation, invariably accom- 
panied with uric acid in the blood, and the deposition of 
urate of soda in the affected tissues.* The positions given to 
the words * specific ' and 4 accompanied ' suggest what was 
probably not in the author's mind. Strictly interpreted, the 



DEFINITION OF SPECIFIC D] 



anguage means—Gout is articular inflammation of a s: 
jharacter (not described); it has, for concomita | 

n the blood, and deposits of urate of soda. Th 
ng must be presumed to be— Gout is articular inflamma 
>pecitically marked by uric acid, &c. 

This definition is one of those advanced general 
attained in some diseases, which penetrate to the < 
features of the disease, without fully expressing the Bympt 
A. detailed account of the symptoms is therefore added, 
under the title 'Description of an attack of Gout, and of the 
progress of the disease' (a sort of popular hist, 
and secondly, under ' Phenomena occurring during an 
Gouty Attack/ where there is a more rigid and Bystei 
analysis into (1) Febrile Disturbance, and (2) Local 
ances. 

Again, Small-Pox is thus defined (Dr. Aitken). ' T 
duct of a specific and palpable morbid poison, which is 
reproduced and multiplied during the course of the malady. 
(1). Afcer a definite period of incubation a remittent lev 
established and followed by an eruption on the skin, 
sometimes on the mucous surfaces, with other concomitant 
and occasionally succeeding affections (2). The eruption on the 
skin passes through the stages of pimple, vesicle, pustule, N 
s'and leaves marks or cicatrices on its site (3). The die 
runs a definite course, and, as a rule, exhausts the suscepti- 
bility of the constitution to another attack (1).' 

Here we have, in sentences (2) and (3), the leadii 
toms of the disease, which, when elucidated at full, make up, 
as far as book description can go, the characters \vh> 
disease is known and discriminated. Sentence (1) 
I properly belong to the definition, but to the predication ; the 
'cause of a disease must always be accounted a p 
! Sentence (4) contains two statements, first, 4 the 
ia definite course/ which surely is true of many other 
; if not of nearly all ; second, 4 it exhausts th< 
the constitution to another attack, 1 a m 
stance, but still better reserved for a predicate or 
than mixed up with the defining marks. 

Influenza is thus defined by Dr. Parkes : — ' I 
specific fever, with special and early implication of I 
laryngo-bronchial mucous membrane ; duration 
from four to eight days ; one attack not 
epidemics.' The transposition of the 
desirable : — • An epidemic fever, specially I 



588 LOGIC OF MEDICINE. 

early implication, &c.' This definition also is a summary o 
Bymptoms, and nothing more. The author proceeds, undci 
the head 4 Symptoms ' to describe the general course of the 
disease, and under ' Consideration of the Special Symptoms 1 
to analyze them in the detail ; Temperature, Condition of the 
SI, in, Nervous and Muscular Symptoms, Respiratory System, j 
Circulation, Digestion, &c. 

All the facts stated in the Definition may be fairly allowed 
as defining circumstances, with the exception perhaps of the 
last ' one attack not preservative in future epidemics,' which! 
might be reserved for predication. Doubtless, if we had a' J 
generalization of the central or fundamental fact of the 
disease, this would take place among deductive consequences, j 
or propria. But we do not need it in a definition consisting! 
of a summary of the symptoms. 

The following sentence commences Dr. Buzzard's definition 
of Scurvy : — ' A peculiar state of mal- nutrition, supervening 
gradually upon the continued use of a dietary deficient in 
fresh vegetable material, and tending to death, after a longer 
or shorter interval, if the circumstances under which it arose 
remain unaltered. ' Here we have first a theory or hypothesis 
of the essence of the disease (a state of mal-nutrition), secondly, 
its cause, and thirdly, an announcement of its dangerous 
character. All this is extraneous to the definition, which is 
given unexceptionably (as a summary of symptoms) in what 
succeeds to the above quotation. 

Propositions of Medicine. 

10. The Real Predications of Medicine, as contradistin- 
guished from the Essential or Defining Propositions, fall 
under distinct heads. 

The coupling of the Essential characters, even although 
numerous, is Definition, and not Real Predication. Nay 
farther ; the modified characters shown in different constitu- 
tions and different circumstances, should be held as a part, or 
as an appendage, of the Definition. Heal propositions may 
arise in connexion with these modifications when certain cir- 
cumstances are alleged to intensify or to resist the diseased 
action. 

11. The first class of Eeal Predications comprises In- 
ferences or propria from the Essential characters of a Dis- 
ease. 



PROPOSITIONS IN M; 

Having given the defining marks, in their ul 
menfc, together with the important modilic itions an,! v 
we can by the help of general principles— P 
Biological, or Pathological— draw many conclu 
on the treatment of the disease. It v> 
ample, to unfold a great many fa 
the Law of Conservation, the laws and 
mistry, &c. The maintenance of an , 
with less than the ordinary nourishment, iuvol 
inanition of the organs, and the format; 
of wasted tissue ; with many other consequence! 
situations. This deductive process, when ba 
ascertained generalities, ailbrds propositions capable 
precision and certainty. 

12. The second class of Eeal Predica 
the Causes of Disease. 

^ A Disease is one thing, its cause is another th; 
tions of Causation, are, therefore, in their na1 
Their importance demands a distinct and separa( 

Implicated with the great subject of 11 
preservation, there is a body of information i 
General Causes of Disease. It is all one thing to ki 
are the means to keep the body in health, and what will c 
loss of health. 

Many forms of disease are clue at once to the d 
between the expenditure and the nutrition of the 
The diseases of exhausted organs — functional v 
degeneration of the muscles, the brain, the stomach, the 1 . 
the heart, the kidney — are of this class. 

To the same general head should be referred near!; 
thing meant by Predisposing Causes oi 
many diseases that do not spring up 
tion from without; called Zymotic Die 
of many (but not of all) such di>eases ma 
healthy system, any circumstances that 
vigour, or weaken particular i 
causes ; as when cholera ; 

intemperance, or by insufficient food, or by ill-\ 
dwellings. 

It is less easv to croneraliz? the va 
as Infection, Epidemic poison, Mia 
great field for Representative Hyp 

Under each separate Disease, an the 



590 LOGIC OF MEDICINE. 

Cause, as far as known, whether general or special. Where- 
ever there is a loss of power from the predominance of waste 
over supply, Causation in Disease appears as ' Conservation ; ' 
it, however, still more largely implicates Collocations. 

13. There may be a distinct class of Real Propositions, 
expressing the effects of Disease. 

The full definition of each disease comprises its whole 
history to the termination ; the temporary prostration of 
Typhus is not an effect of the disease, it is the disease itself. 
When, however, a disease, besides accomplishing its course, 
makes permanent changes in the organs or constitution of the 
patient, this is a distinct fact, and may be enrolled under the 
head of Causation. Such are the after effects of Small Pox, 
Measles, Scarlet Fever, and Syphilis. While a few diseases 
hare a wholesome efficacy, the greater number weaken the 
system at some point, and are therefore predisposing causes of 
future disease. 

14. The Remedies of Disease constitute Real Propositions. 

All the previous classes of assertions prepare the way for the . 
present. The remedy of a disease may be suggested by its 
Characters, whether primary (Definition), or inferred from the 
primary (Propria) ; or by its Causation, on the principle of 
4 remove the cause.' Diseases of functional degeneration, or 
premature decay of organs, involve in their cure 'repaying 
the debt to nature' — the restoration of the balance of nourish- 
ment and waste. 

In many instances, the remedy consists in something differ- 
ent from either treating the symptoms, or removing the cause. 
The Specifics that have been discovered for particular diseases, 
as quinine, colchicum, lime juice, cod liver oil, are affirined as 
independent facts, resting on no deductive inferences from 
Cause and Effect in Disease, but on the experience of their 
efficacy. 

TJie Experimental Methods in Medicine. 

15. All the Experimental Methods are applicable to 
Medicine, with certain cautions and qualifications. 

The ultimate problem of Medicine is to find a remedy for 
every remediable disease ; and the apparently direct solution 
is to try various remedies upon actual cases. If by Agreement, 
under a wide variation of circumstances, a certain remedy ife 



THE EXPERIMENTAL Ml 11MD3. 

bund to succeed uniformly, or in a great ; 1 of 

nstances, there is proof that it is the remedy. 

Still, we cannot but remark the very serious diflicul 
ttset all the Experimental Methods in thisath 
>f Causes and Intermixture of Meets occur in the mo 
rated shape. Moreover, drugs, beii il Kinds, 

many possible ways of acting, that the oliinin the 

precise property that affects the system is all but bopi 

AVithout, therefore, abandoning the tentative , as 

applied to actual disease, modern medicine 1 
sjeously approached the problem in circuitous ways ; and 
instituted researches where the experimental me! 
likely to be defeated. Thus — to take the example that dej 

[least from the empirical method — the mode of action of 
medicines and of remedies is studied by experiments, no! 
stricted to special diseases, but applied to the system in health 
and in disease alike, under every variety of conditions, Thia 
is a far more thorough and searching procedure; and tho 
Method of Agreement will, of itself, give trustworthy result* 
under so great an extension of instances ; while by superad- 
ding Difference, Inverse Agreement, and Variations, there 
may accrue results of the highest certainty. I may cite, among 
this class of Researches, the Report of Dr. Bennet on the 
Action of Mercury on the Biliary Secretion, and Dr. Har 
work on the Old Neurotics. By such researches is built up 
that part of Materia Medica relating to the Therapeu! 
of medicines. 

Again, the Pathology of Disease, the concurrence and 
quence of symptoms, studied, in the first instance, apart from 
modes of treatment, is open to experimental enquiry, and 

J lead to results having all the precision attainable 

I science of Medicine. For such enquiries, the Experim 
Methods are suitable ; the endeavour being 
each one of them into play, by searching for 
riate class of instances. Mere Agreement is usually 
sno-o-ests itself to the untutored mind ; the f 
in Absence and of Variations is apparent on: 

' have reflected largely on the conduct, of scientin 
The influences commonly called Hygienic, 
Therapeutic agencies, as cold and heat, 

: rest, stimulants, Ac, not only ] ' difficult! 

periment, but are also within tb 
method. In like manner, the proof of noxious 
impure water, and the effluvia of decay-is easy and con:. 
26 



592 LOGIC OF MEDECINE. 

16. The Elimination of Chance is of great value ii 
Medicine. Its groundwork is Medical Statistics. 

Nowhere more than in Medicine may laws, of Causation bt 
defeated ; there is rarely such a thing as a simple cause yield- 
ing a simple effect. Hence, the necessity of ascertaining 
whether a coincidence is more frequent than would be ac- 
counted for by chance. The cinchona bark sometimes fails tc 
cure ague, yet its general efficacy is satisfactorily established. 

To prove the efficacy of medicines as a whole, in opposition ' 
to some speculators that ascribe all cures to nature (aided by 
repose and regimen) the physicians of a French hospital ; 
made the experiment of withholding drugs from all the patients 
for a certain time. The conclusion seemed to be that the 
mortality was not increased, but the recoveries were more 
protracted. This was a competent inference from statistics. 

The difficulties in obtaining a statistical proof of the action 
of a remedy in a given disease are exactly those already 
mentioned respecting the use of Agreement in the same* 
determination.* A large hospital statistics is better than the 
inferences of a single physician in private practice, and yet 
may come short of the proof. There should always be obtained, 
if possible, a parallel statistics — cases with, and cases without,^ 
the treatment in question. The statistics of cholera treatment 
may be alleged in favour of many modes ; but none appear to 
be decisively established. 

Statistics, as applied to Scarlet Fever, has shown that a 
second attack is extremely rare ; that the ages of two and 
three are most susceptible to the disease ; and that the maxi- 
mum of prevalence is in October, November, and December,' 
and the minimum in April, May, and June. 

The Deductive Method. 

17. The scope of the Deductive Method in Medicine is 
co-extensive with the number of well-established generali- 
ties than can be appealed to. 

The sciences applicable to Medicine — Physics, Chemistry, 
and Biology— yield a considerable number of these fertile 
generalities. The science itself contains few of a very com- 
manding character, but a considerable number that have a 
sufficient range for deductive operation, and for converting 
empirical into derivative laws. All the propositions of general 

* See an estimate of these difficulties in Dr. Barclay's work on Medical 
Errois, p. 35. 



HYPOTHJJ 






causation in medicine, the lav, 

laws of the action of drags on the s 

sufficient breadth to control and c 

and the mastery of these, as well as of the i 

principles of the preparatory 

the physician. The physiology of J 

forces of the system, muscular, heat-giving, 

and the products of elimination,— is pregnant v. 

consequences, both in warding oiF ami in curing 

The experimental methods are greatly a: 
acting causes; and hence deduction is pre-eminently 
in such points as the influence of alterative 
lants, climatic influences, and modes of life. Only a thon 
going statistics, or a deduction from general principles, 
dispose of the doubts that arise on such points. 

Hypotheses in Medicine. 
18. Medical Science is largely dependent on IIv; 

As a department of applied Biology, Medicine needs all the 
aids rendered by hypotheses in the mother science, and 
special to itself. The great biological fact — Assimilati 
takes on a new aspect in the production and spread ol 1 1 

The first and simplest case of Hypothesis, the assuming 
an agent known to exist, but not known as present i:, 
quate amount in the given case, is abundantly exempl 
Thus, the origin of contagious disease is ascribed hypol 
cally to various real agents, and among othei 
living organisms. The effects tally in a general way 
such an agency. What remains is to find whether t 
closely at all" points. The hypothesis, however, r 
powerful support from individual cases where tl 
an animalcule, or living germ, appears to be a 
lished. The alternative, and older, hyp 
particles, in a state of change or activity, an 
one living body and infect another, such j 
complete organisms or the \ 
thesis may seem to assume \c,s than tin 
it assumes a class of particles i octly pr< 

A strong analogy may be pleaded 
communication of morbid action wil 
of the poison of small pox must be the same 
of the innoculated patient as on the original pati 
aerial effluvia of typhus may consist of B ►methiug more 



591 LOGIC OF MEDICINE. 

definitely organized than the supposed active particles. Fer- 
mentation by yeast is found to be due to an animalcule. 

The Representative Fiction is indispensable in Medicine, 
and its rules and properties need to be well understood. 

Diseased appearances, like all manifestations of living bodies, 
are the superficial outcome of a vast concatenation of hidden 
changes. These intermediate links are in great part unknow- 
able ; yet, by following the clue of what we know, we may so ' 
conceive or imagine them, as thereby to unite the appearances 
in a consistent whole. When an organ is liable to derange- 
ment from slight causes, we pronounce it weak, which is merely 
to express the fact in another word ; when, however, we assign 
such circumstances as that its tissue has degenerated or 
changed, that it has very little tendency to assimilate nutri- 
ment from the blood, or that the superior exercise of all the 
other organs of the body withholds from it the fair amount of 
blood and nerve force, — we employ convenient hypotheses, 
which are more or less in keeping with the facts. 

As regards the two leading diseased processes — Fever, and 
Inflammation — probably no hypothesis yet framed adds any- 
thing to the facility of conceiving or of generalizing the facts. 
Supposing the different fevers generated each by a specific ; 
virus, or animated body, we cannot even in imagination sup- 
pose a connexion between the structure of the infecting i 
element, and the specific characteristics of the fever ; as in the 
difference between typhus, scarlet fever, or intermittent fever. 
Indeed, we cannot form a plausible supposition as to the 
intermediate link that connects a certain infecting substance 
with the febrile state generally. The difficulty here is exactly 
the difficulty in representing the facts of living action. 

Hypothesis appears to more advantage in connexion with 
what is termed Functional Degeneration, Functional weakness, 
strength and weakness of parts. Great convenience attaches 
to the use of such phrases as healthiness, robustness, vigour, 
constitutional force — which are modes of stating the absence 
of disease under circumstances that usually provoke it. We 
may increase the value of this class of terms, by hypothetical 
interpolations, to the following effect : — 

Assuming an average healthy system to begin with, we 
know by reasonable inferences, (1) that every one of the organs 
needs an equable supply of blood, with more or less aid from 
the nervous centres, and (2) that each organ is capable of a cer- 
tain amount of exertion. Suppose now, ihat by any cause, 
either the nutrition is below the mark, or the exertion above 



HYrOTHESIS OF DEGBNJUULT* 

it, or both. It is the nature of the system no! I 

mediately the effects of such a niiii-proportion, \ 
, he an immediate effect; the overwork, or tho d< 
\ tion, of a single day does not leave the organ 

we are entitled to assume that there is superiiid i 
I structural change, or degeneration, perceptible on many 

repetitions, but actually realized. Suppose the 

of expendituie and supply to continue for a length 
1. the first outward symptoms will probably be, that the 

enfeebled in some duty that is required of it, and 

positively disordered under influences that, in its re" 
I dition, it would have successfully resisted. A 

degeneration or structural change lias made a d< 
I vance ; another equal advance would bring down the 

the bare performance of its functions; a third would 
I suspension and death. Now, we have here scope I 

great variety of. suppositious, as to the relal litiou 

I of all the organs in the body. We can represent the 
tional peculiarities at birth, by the proportionate dU 
of the several organs — nerves, muscles, lungs, dige 
appropriate nutriment, and to become vigorous or t 
site ; we can state to ourselves the practical mode of redre 
the inequality, namely, by restraining the vigorous organa 
their tendency to impoverish the rest, and by giving 
opportunity to the nourishment of the weak. We can 
the rationale of the constitutional treatment of disc.! 
the placing of the weakened organs in such a position B 
increase their nutriment and abate their over-exertion. We 
can give a hypothetical account of the degeneration oi 
gans such as the heart and kidney, which oil en show 
signs until the structure has reached a mortal diseaf 
should, moreover, feel no surprise at the sudden breaking down 
of constitutions reputed strong ; the popular eye 
prosperity of those organs that cast a dash and 
muscles, the stomach, and the brain. The d< 
closes the degeneracy of the heart, the lui 
following on the very strength of these ostentatious men 
of the system. 

Classification of i 

19. There being upwards of one thousand re 

Diseases, they may, like other great I come 

under a regular Classification. 



596 LOGIC OF MEDICINE. 

Diseases may fall under a classified arrangement., like 
Minerals, Plants, or Animals, attention being given to the 
peculiarities of the department. 

I. Order of Characters.— In Mineralogy, and in Botany, a 
strict order of characters is observed. This is disregarded in';] 
Zoology, and also in Medicine, from difficulties that can be 
readily assigned. There is every likelihood, however, that- 
both sciences would gain by a systematic arrangement of char- i 
acters, avoiding the sacrifice of the spirit to the letter. 

In a work to be afterwards referred to (p. 597), the remark 
is made ' that the labour of analyzing and comparing clinical ij 
observations would be greatly lightened, and the precision of 1 
the observations themselves increased, if the records of these 
were in every instance arranged on an uniform plan.' 

One obvious precaution is to make the outward symptoms 
precede the subjective. Thus, of the usual marks of inflam-u 
mation, the pain should come last. In nervous diseases, thel 
physical symptoms should be fully enumerated before entering jjj 
upon the mental symptoms ; the two classes are then viewed in i 
such a way as to check and confirm each other. 

II. Maximum of Affinities. — • The propriety of classing 
Diseases by their closest resemblances is sufficiently allowed i 
in the abstract ; the difficulties in execution are not logical, fj 
but pathological. 

III. Arrangement by Grades. — The formality of Grades is 
observed in the classification of Diseases, but without the full j 
carrying out of what it involves. There is something of lax- i 
ness attending the use of the method even in Chemistry, the 
statement of the points of community of the higher grades 
being sometimes given, and sometimes not, without any 
apparent reason. 

Occasionally there is vacillation as to w T hether diseases are 
different in species, or mere varieties. Little importance 
(attaches to the question ; and the workable criterion is the \. 
comparative number and persistence of the distinctive marks. 

IV. Statement by Agreement and Difference. — Everything 
already said on this head applies to the exposition of Diseases. 
The systematic and orderly stating of Agreements, and the j 
pointed contrast in Difference, have the same efficacy here as 
elsewhere. Under the heading 'Diagnosis/ it is usual to I 
mention the closely resembling diseases, and to indicate the 
diagnostic marks. For example, Roseola is distinguished 
from Scarlet Fever, thus : — the eruption in Roseola is gene- 
rally confined to the chest. When the diagnostic points are 



INDEX CIASSmCATlON. 



two or more, they might be set forth in the foi 
already exemplified. 

20. V. Index Classification. — For Medicine, an ; 
Classification might be provided on the tabular pi 

This aid to the discrimination of Dis< 
Probably, it would be best attempted, in the first inal 
the tabular plan. A basis is afforded in a small work, p 
lished by the Medical Society of Observation, with the utlo 
' What to Qbserve in Medical Cases.' 

The work professes to lay out in order an exhaust i. 
ment of all the appearances connected with each bodily or 
besides adverting to the external circumstances of the 
The enumeration commences with the Skin, which is iollowd 
by the organs of Locomotion, Digestion, Respiration, I 
tion, Lymphatics, Urinary Organs, Organs ofGenerah 
and Nerves, Vascular Glands. 

As an example, I quote the varieties of the Pul Ud 

Pulse.— number ;-size and force; large, small, thready, • 
unequal, strong, feeble ;-resistance ; soft compressible, . 
incompressible ;-rbythm; regular irregular, ******* 
time as compared with that of heart's impulse part,, J 
rigid.-Special characters of pulse; jerking, boumlmg u , 1 : 
tory, continuous (one pulse appearing to run into the fc U 
vibrating, quick, tardy, vermicular tremulous red 
Effects ol posture on pulse (its number and other ch r 
Phenomena of pulse in one arm as compared with 1 

The authors have evidently studied exhau 
be-in with. It is possible, however, to be too mi 
EctTons that are not marks of anything 
and mav be an encumbrance. The next, step, 
should be to abridge and group the symptoms with 

tet2| oSeTa methodical array of , 
under each or°gan, the mode of proceeding With a V, 
Index is to append to each symptom a list of u . . 
where it occurs. Should a symptom appea a i • 

disease (as urate of soda in gout) the occurrenc 
torn would decide the disease at once Slion 
appear in three diseases, its occurren 

three diseases. r ,.,j n ,, in <li 



598 LOGIC OF MEDICINE. 

four diseases ; a second symptom leads to another list. If on 
comparison, there is found only one disease common to the 
two lists, the diagnosis is complete. If there are two or three 
common to both lists, a third symptom must be sought out 
with its corresponding entries, by which the alternations are 
again reduced ; and so on, till the concurrence of symptoms I 
points to a single disease. 

Suppose, for illustration, that * Irregularity of the Pulse ' 
appears as symptom. According to Dr. Watson, this may I 
attend (1) disease within the head ; (2) organic disease of the 
heart ; (3) simple disorder of the stomach ; (4) debility, and 1 
a prelude to stoppage of the heart's action from asthenia. 

Now supposing the tabulation of symptoms and of diseases 
complete upon this plan, and supposing a second symptom in 
the case under enquiry had opposite to it a list, agreeing with 
the first only in the entry ' simple disorder of the stomach,' 
the diagnosis is made out by two easy references. 

Owing to obvious causes — the great number of diseases 
accompanying particular symptoms, the occasional ambiguity 
of actual diseases by the failure of some of their usual symp- 
toms, and the imperfection of the terminology of symptoms, — 
the best scheme that could be given would be imperfect. 
This would not, however, prevent it from being a boon to the 
student, and an occasional aid to the experienced practitioner. 
It does not supersede, but indicates, the reference to the 
systematic works on Medicine and Pathology, which are the 
authorities in the last resort. 






BOOK VI. 

FALLACIES. 



CHAPTER I. 
MILL'S CLASSIFICATION OF FALLACIES, 

Mr. Mill regards all fallacies as divisible iul 
heads — Fallacies of Simple Inspection, and Fallacies of I 
EXCE. By the first class he understands those i 
presumption is created in favour of a fact or doctrine, on 
mere inspection of it, and without any search for c 
natural prejudices are comprised under that bead. I». 
second class he understands erroneous conclusV 
posed evidence. This class is subdivided accord in 
nature of the evidence simulated ; which may be (i 
inductive, &c. A special division is indicated under the 
'Fallacies of Confusion/ where the error a 
link between premises and conclusion, but in ; 
handling of the premises themselv 

There are thus five distinguishable classes of Fallac; 
forth in tire table : — 

of Simple Inspection - 1 . Fa U 

flndacti 

from evil oncel., u • < 
distinctly ) FaUaai tnUmOm 



/ Fa.lL 






| 
I 



5. F 
of Inference/ 
I. Fallacies of Simple I* 
framing from the discussion of the i 
nation might raise, what are the ultima 1 



GOO MILL'S CLASSIFICATION OF FALLACIES. 

the foundation of all reasonings, Mr. Mill adduces first th< 
tacit assumption that the same order obtains among the objects 
of nature as among our ideas of them — that if we always thinL 
of two things together, the two things must exist together 
He illustrates this tendency by numerous popular superstitions 
as 'talk of the devil and he will appear/ &c. He also cites— 
the philosophy of Descartes, which, from the mere conceptions I 
of the mind, inferred the existence of corresponding realities:! 
the doctrines that ' whatever is inconceivable is false/ 4 that 
a thing cannot act where it is not ' (applied by Newton tc 
show the necessity of a gravitating medium), that * matters 
cannot think/ that * space is infinite/ that ' nothing can beS 
made out of nothing/ that 'nature always acts by the simplest 
means.' An allied Fallacy, or prejudice, is the tendency tc 
presume a correspondence between the laws of the mind and 
the laws of external things, of which one form is expressed! 
thus : — ' whatever can be thought of apart exists apart/1 
From this springs the personifying or re-ifying of Abstractions,; J 
as in the doctrine of Realism, and in mystical theories gene-^ 
rally, whether it be the mysticism of the Vedas, or the mysti- ^ 
cism of Hegel ; all which proceeds on ascribing objective 
existence to subjective creations — feelings, or ideas. 

Another kindred fallacy consists in representing nature as 
under the same incapacity w T ith our powers of thought ; the! 
great example being the celebrated Principle of Sufficient 
Reason, adduced in explanation of many first truths, such as 
the laws of motion. 

4 That the differences in nature correspond to the received 
distinctions of language/ is another wide spread and baneful 
prejudice, which particularly weighed upon Greek philosophy, 
being prominent in the reasonings of Aristotle, and from which 
Bacon was unable to set himself free, as is shown by his futile 1 
attempts to find a common cause for everything that goes 
under a common name, as heat, cold, &c. 

Lastly, there has existed the prejudice that ' the conditions 
of a phenomenon will resemble the phenomenon ' — like pro- I 
ducing like : as that motion must necessarily arise from the 
impact of a moving body ; that a sharp taste must be brought 
about by sharp particles ; that our sensations must be copies 
of external things; that the law of causality can hold only 
between what is homogeneous, whence there can be no causa- 
tion between mind and matter ; that the Deity must have the 
exact perfections discoverable in nature. 

II. Fallacies of Observation. — These do not apply to the 



GENERALIZATION. — RATIOCINATION, 

operation of observing, for which there is i 
called, bat to the omissions and partialities in c 
With a view to the generalizing process. T 

* observation, or Mal-observation ; the one Leaves out 
i instances, the other distorts or misrepresents wh 

* Non-observation explains the credit given to fertm 
I to quacks, and to false maxims ; tho cases foi 

I noted, and the other forgotten. The motive in tin 

I fallacies is a strong pre-conceived opinion or wish fee 
dictum true. Farther, the Non-observation may be, D 
instances, but of material 'circumstances, as when it 

t that lavish expenditure alone encourages industry, the cir 
stances being overlooked that savings arc capital 

| employment of labour. 

Under Mal-observation may be placed tho chief mistake 
connected with the proper act of observing, namely, the 
founding of a perception with a rapid inference, or the mm 

. up of inferences with facts. This is the common infirm 
uneducated witnesses and narrators of events. 
. III. Fallacies of Generalization. — These are errors in 

* employment of the Inductive process. The chief inst: 
adduced are these: — All inferences extended to remote parte 
of the universe, where no observation or verification can be 
carried ; all universal negatives and propositions asser 
impossibility (not being contradictions in terms) ; the the 
professing to resolve all things into some one element, of which 
the most notable instance is the attempt to resolve star- 
consciousness into states of the nervous system ; the pla 

of empirical laws, arrived at per enumerationem simplia 

the footing of laws of causation, largely exemplified in 

ings upon society ; the vulgar form of the same i 

nated post hoc, ergo propter hoc ; and the fertile class of 1 

Analogies. Under the same head are specified Bad C 

tions, or the asserting under one terra, things that have little 

or no community ; of which the Greeks gave examples in 

terms as Motion, Generation and Corruption. 

IY. Fallacies of Ratiocination. These comprise the e: 
against the laws of the Syllogism. Mr. Mill, however, property 
includes under them the fallacies connected with the Con 
sion and Equipollency of Propositions; remarking that tho 
simple conversion of the universal affirmative, and th 
ous conversion of Hypothetical are among the D 
sources of error. Of this last class, is the maintenance of .sumo 
favourite doctrine, on the ground that tho inferences fro: 



C02 mill's classification of fallacies. 

are true. Connected with the Opposition of Propositions is 
the confounding of the contrary with the contradictory of a 
Btatement. Vicious syllogisms, whether from undistributed 
middle, or from illicit process, are the more noted instances of 
this class of fallacies. There may be also included the fallacy 
of changing the premises, occurring frequently in the argument- 
ative discourses of unprecise thinkers (the schoolmen's a dido 
secundum quid ad dictum simpliciter) ; exemplified in the once 
favourite theory that ' whatever brings in money enriches.' 
Under the same head might be placed the misapplication of 
general truths, or the supposition that a principle true in the 
abstract must hold under all sets of circumstances. 

V. Fallacies of Confusion. The first class under this desig- 
nation is Ambiguity of Terms, As there is no limit to that 
form of confusion, a logician can only select a few random 
instances ; those chosen by Mr. Mill are ' scarcity of money/ 
4 influence of property,' 'theory,' 'the church/ the 'laudable' 
in a Stoical argument in Cicero's De Finibus, ' I ' in Descartes' 
argument for the being of God, ' necessity/ ' same,' ' force/ 
4 infinite/ ' right / to which he adds examples of the fallacy 
of Composition and Division, as strictly belonging to the same 
class. 

The second division is Petitio Principii, otherwise called 
* arguing in a circle/ of which there are abundant examples. 
A certain species of terms received from Bentham the desig- 
nation ' question-begging appellatives/ because they begged a 
question under the guise of stating it ; such is the word fc Inno- 
vation.' Plato, in the Sophistes, has an argument to prove 
that things may exist that are incorporeal, because justice 
and wisdom are incorporeal, and they must be something : 
thereby begging the question that justice and wisdom are 
things existing apart or in themselves. One of the most re- 
markable examples of fallacy is furnished by the political 
theory of Hobbes and Rousseau, known as the theory of the 
' social compact.' We are supposed bound by the promise 
entered into by our ancestors before society was called into 
existence ; but there is no such thing as an obligatory promise 
until society has first been formed. 

The third class of Fallacies of Confusion is the Ignoratio 
Elenchi. It is exemplified in most of the replies to the popu- 
lation doctrines of Malthus. A still more signal instance is 
the stock argument against Berkeley's doctrine of the non- 
existence of matter ; Johnson's kicking the stone was not the 
point denied in the ideal theory. 



CHAPTER TL 

THE rOSITIOX OF FALL\rr 

The setting apart of a distinct chapter to i 
of the errors against the laws of reasoning 
at first sight an incongruous proceeding. 
a law from its violations ; the one implicates the othi 
good reasoning is exhibited, there must be exhibil 
same time the coresponding bad reasoning, it' the m 
given that the middle term of a syllogis 

once, whoever understands the rule must coi t the 

same time, cases of its fulfilment and cases of its non-fulfil- 
ment. If the method of Difference requires that the i 
compared shall coincide in every particular save 01 
instructed by it that the method fails if any 
not coincide to this extent. If a good classification inv 
identity on one or more points of importance, there is ii 
in the same statement that a grouping under one nam", with- 
out any important community, is a bad classificati 
* fallacy ' of classification. 

Any one would recognize the absurdity of a grammar 
would reserve for a chapter at the end all the 
grammatical errors. Yet such is apparently the plan pu 
in Logic. The grammarian, ind< icntly p 

separate collection of errors by way of pr 
but these are additional to what necessarily and 
occur under the rules that they sev 
ever, is not avowed by the log 
chapter on Fallacies. 

Without entirely exonerating works on Logic fi 
inconsistency of distributing 
subject the fulfilment and the vi 

can assign certain circumstances thai fl- 

ing usage. The main circu 
fietd of logical precepts, froi 
generation. The 
almost exclusively restricted to 
departments; hence, in the exe:: 
errors could come to light excej 



(]0i THE POSITION OF FALLACIES. 

of syllogism. But the Greeks had surveyed human knowledge 
wide enough to be aware that many errors passed current 
that could not be reduced to errors of syllogism. The logician, 
therefore, was driven to one of two alternatives — to make no 
allusion to some of the most notorious failings and mistakes of 
the human understanding, or to provide a chapter for enumer- 
ating such mistakes entirely apart from the body of logical 
theory. It was characteristic of Aristotle to choose the second 
alternative— to be inconsistent rather than to be incomplete. 
His treatise on Fallacies comprises errors against the Syllo- 
gism, which he could not omit noticing under the Syllogism 
(Undistributed Middle, Illicit Process) ; but these are a small 
part of the mass of Fallacies ; and the rest he had not 
any theory for. He had no Inductive Logic (or only mere 
traces which his followers wiped away), and therefore he had 
no place for the exhibition of the rules sinned against by post 
hoc, enjo propter hoc. For want of a thorough-going discussion 
of the department of Classification and Definition, he could 
not exhibit the errors connected with general language under 
precepts for the classifying of things and the denning of 
terms. 

It has been seen, however, that even the thorough-going 
Logic of Mr. Mill does not dispense with a * Book' on Fallacies. 
This is explained in part, but only in part, by the author's 
adhering to the usage of all former logicians, while using his 
own extended system to re- arrange the recognized examples, 
and to introduce new ones. Yet all the fallacies in the 
second, third, and fourth classes (Observation, Generalization, 
Ratiocination) might with the utmost propriety be absorbed 
into the body of the work. The account of the inductive and 
deductive processes unavoidably quotes derelictions from the 
sound performance of these processes, which derelictions are 
identical with the fallacies treated of under the heads just 
named. 

The case is different with Mr. Mill's first and last classes 
(Simple Inspection and Confusion), The chapters on these 
heads contain matter that would not readily find a place in 
the systematic exposition of the logical methods. To take the 
first class, Fallacies of Simple Inspection, or a priori. Under 
these, the author dilates on certain fallacious tendencies of 
the mind, the generating causes of errors. Now, the logician 
might say that his business is to show how errors are to be 
checked and corrected, not how they arise in the imperfections 
of the human constitution. If he is to handle this ~subject> he 



NATURAL CORRUPTION 01 THE 1M; 

could not with propriety take it Q p in 

Deductive and Inductive Methods; , 

allowed a corner apart. The demand is irrc 

be most inexpedient to agitate, under t 

the Experimental Methods, enquir 

dencies ot the natural mind. Granting that all the d 

and inductive fallacies, and the mistakes of claa 

definition, were taken up into the main body oi 

fallacies a priori, if included at all, mu 

handling. Some doubts might be raised a* 

title or obligation to enter upon the subject, ba 

be none as to his allocating a distinct chapter to the c 

tion of it. 

Socrates was the first person to urge Btroogly 
corruption of the human intellect, and the 
severe remedial discipline, which, in the sua p. 
cross-examination, he was wont to apply to his : 
ians. The theme was not again taken up in a 
manner, until Bacon composed the first book ol 
Organum. The elucidation of the inevitable mi 
the untutored understanding, intellect us sibi ; 
classification of idola — false lures, in that renown- 
instead of being laid to heart and followed up by 
amples, became a matter of mere parrot repetiti -a. ] 
person to treat the subject independent! 

cally over the ground, was Mr. Mill, in his ch tied 

' Fallacies a priori.'* So important is the so 
far is it distinct from the proper field of L >gic, thai 
be embodied in separate treatises. It is a kind of homil 
preaching, a rousing address on human frailty ; and altfa 
the logician is the person most likely to be impressed wi: 
evil consequences, he is not the only pel 
trate them ; while the points to be adduced in t 
are not precisely such as tall under cither the deductive or the 
inductive logic. 

Mill's concluding head ' Fallacies i 
extra-Jo jical. The extension )f the field of log 
this class to be absorbed. They cannot 1 m 
inductive, any more than deductive precepts. I 
are owing to the defective acquaintance wi:h I 
of the reasonings, and to a low order of i 
generally, rather than to misappreb 
considerable stretch of the logician's | 
the taking up of this class of errors, ] ind thai 



COG FALLACIOUS TENDENCIES OF THE MIND. 

cover is boundless and indefinable ; no man can foreshadow 
the intricacies, the incoherences, the perplexities, the entangle- 
ments, possible to the human understanding. The only 
circumstance that justifies the attempt to handle them syste- 
matically is the great frequency of a few leading forms ; in 
consequence of which they can be, to some extent, treated 
comprehensively. Mr. Mill's three classes of examples — 
Ambiguous Terms, Petitio Principii, Ignoratio Elenchi — have 
this character of extensive recurrence. Moreover, in the 
elucidation of such classes, there come to view many prominent 
and practical errors, thus opportunely laid bare. 

From these considerations, it follows that the most defensible 
course to be pursued in regard to Fallacies is to absorb into 
the main work all those that are the direct violation of logical 
precepts ; and to handle, in the chapters apart, the Fallacious 
tendencies of the human mind, and the Fallacies of Confusion. 
This is not to debar the assembling of additional examples in 
a supplement or appendix ; it being understood that these are 
merely in continuation of the examples already furnished in 
the regular course. 



CHAPTER III. 

FALLACIOUS TENDENCIES OF THE MIND. 

. The Fallacious tendencies of the mind may be traced through 
an enumeration of the sources of Belief. 

The state of Belief is a form or manifestation, of our activity. 
The import and measure of Belief is the readiness to act in tho 
direction indicated by the thing believed. A man's belief in 
the wholesomeness of a regimen is shown by his energy and 
persistence in adhering to it. 

There are three distinct sources of belief. I. The inherent 
Activity of the System — the disposition to act through mere 
spontaneous vigour. II. The influence of the Feelings, 
Emotions, or Passions. III. The Intellectual Associations, cr 
acquired trains of thought. Excepting under the last head, 
there is nothing to guarantee soundness of belief, or the accord- 
ance of the thing believed with the reality. 



OUlt EAKLY BELIEFS OVRB-VA 

I. Inherent Act lei 1 

From the spontaneous ami inherent vigour of th 
are induced to act somehow, to change out o 
the active condition, ami to continue that actn 
energies are unexhausted, and while there is free I 
struction. There is no enquiry beforehand 
course or direction to act in ; opposition is no! pr 
actually encountered. A way now open is su 
ways open; the mind does not anticipate any future termin 
or obstacle^ Blind confidence is the primitive attitu 
mind. It is only through the teaching of ex 
suppose any limit to our career of action. 

This state of mind shows itself in our early beliefs, \\ 
may be described generally as over-vaulting; as presum 
that what holds now and here, will hold then ana 
everywhere. The following are instances : — 

We are disposed to assume that, as we feel at the 
moment, we shall feel always. After a certain nnmber of 
checks, the tendency is somewhat restrained, but it conti 
very strong all through early life, and is seldom e 
conquered at any age. 

We begin life by reckoning with the utmost confidence that 
other persons feel exactly as we do. After lengthened 
ence, this primitive tendency is greatly subdued, althou 
perhaps in few minds is it fully sobered down to 
of the actual facts. The consequences are shown in our 
allowing for differences of character, in our inability 
conceive of types departing widely from ourselves, Without 
being the sole origin of intolerance, this tend • itly 

ministers to that prevailing vice of mankind. We 
difficulty avoid judging all men, in all circm I, by the 

standard suited to ourselves and our own circumstanc 

From one or a few instances we are ready to 1 Hf 

applicable without limit. The mere infant parodii 
tive process ; the most ignorant of human beings 
most unrestrained generalizes. From an acquaint u 
one or two Frenchmen, Italians, or i 
characters of the entire nation. We feel 
remedy found to answer in a particular case will answer uni- 
versally. Happening to visit a place during fine 
are led to suppose that the weather there is alwa; 
word ' always ' is a familiar expletive to vent ou: 
temper. 



60S F^LIACIOUS TENDENCIES OF THE MIND. 

We presume that the state of things familiar to us, prevails 
everywhere. Not only are we indisposed of ourselves to 
anticipate and conceive different arrangements, natural and 
social, but we hold out against the very existence of such. 
The king of Siam's energetic repudiation of ice was a genuine 
display of the natural man. 

Without making formal generalizations upon a single in- 
stance, we are disposed to outrun our facts, to extend the 
present into the distant and the future. It is always more 
congenial to make leaps in the dark, than to abide strictly by 
what we actually know. We have no sympathy with any one 
proposing to restrain gravitation to the solar system, where it 
. can be proved to operate ; our natural desire is to extend it 
everywhere, with or without positive evidence. 

To identify, to assimilate, to generalize, constitute one of 
the two great functions of science. Yet there is often a 
necessity for restraining the too great ardour for these pro- 
cesses. We identify and assimilate, without real likeness, 
thus giving birth to bad analogies, and irrelevant comparisons ; 
we over-assimilate and over-generalize. We rush blindly on 
the search after Unity, Simplicity, Fraternity. 

It is a result of the primeval tendency to follow out a lead 
to unbounded lengths, that we so strongly assert the Law of 
Causation, irrespective of the facts that have gradually estab- 
lished its certainty. We have a subjective assurance that bears 
no proportion to the objective proofs. We shall never be in a 
position to assert the law, by the force of legitimate evidence, 
with the confidence that we feel respecting it. 

That human nature is the same in all ages is affirmed, not 
from a careful examination of the records of the human race, 
but because the affirmer has not laid himself in the way of 
checks to the natural tendency to reason from the near to the 
distant. The doctrine is more behoven to ignorance than to 
knowledge. 

The most of Mr. Mill's Fallacies of Simple Inspection are 
referable to the tendency now discussed. That ; we should 
make our thoughts the measure of things,' which is done in 
so many celebrated speculations, is the result of the inherent 
pushing activity of the system, the determination to proceed 
in a course once entered on, until a check is met with, and 
even in spite of a good many checks. ' That the conceivable 
is necessarily true,' and ' the inconceivable necessarily false ' 
are merely various expressions of the same fact. 

The supposition that 4 the effect resembles the cause/ that 



PERVERSION OF THE KBUft 

| Hike produces like' also grows out of tli 
tendency to assimilate, or identity, the repuy 
from a familiar type until compelled by a power from 
The reasonings of ancient philosophy frequently exhibit 
fallacy, especially in the subject where it baa mosl freq i 
operated, the relations of mind and body. i 
reasons that Intellect, as well as Sense — uiusl be oorp 
since it has to deal with corporeal things ; Q bo 

comprehended only by Like. 

II. Influence of the Feelings. 

The perverting influence of the Feelings, in matters of truth, 
has been more generally noticed, than the perversion 
inherent activity. That men have in all ages been biassed by 
their interests, their fears, their antipathies, their likil 
poetic ideals, their religious sentiments, — is one of I 
widely-received and least contested doctrines of human in 
Many of Bacon's Idola are prejudices of the feelings ; the 
idola theatri relate to the poetic, artistic, or ideal en 
the mind ; the idola tribus (which would properly include the 
other) comprise all the fallacious tendencies common bo 
generally, in opposition to individual peculiarities 
they therefore necessarily include the feelings. Mr. Mill [ 
fewer illustrations of the influence of feeling, than of I 
ence of activity as above explained. 

The operation of the feelings is partly through the 
partly on the intellect. What gives us pleasnre I 
ibrits pursuit; and our activity, in whatever w iy p 
carries belief with it. We believe that the thing 
are free from harm, if not beneficial — our fav 
stimulants, amusements. The effect of liking is to in 1 10 
in a given course, which is a power for belief, able to sarin 
a certain degree of hostile evidence. 

The obverse is also implied. What offends, annoy 
pleases us is avoided ; the will is against it ; and \\ 
corresponding difficulty in believing it to be a pr 
pursuit, or in any way commendable. 

The other mode of working on the faMu^ is 
Intellect, A strong feeling, whether pleasnrabl 
occupies and detains the thoughts, and excludes 
all other subjects. If it be pleasurable, 
maximum; but even pain has power to 
under great excitement, thoughts alien to tl 
of the time, are not allowed to rise to the view; wo ] 



CIO FALLACIOUS TENDENCIES OF THE MIND 

upon one-sided facts and views. An orgie of pleasure renders 
us unable to entertain disagreeable facts ; a fright allows us to 
see nothing bat danger. 

The present purpose will be served by the following enume- 
ration of perverting states of feeling : (1) Self-interest gene- 
rally; (2) Sympathy; (3) Special Emotions. Such is the 
order found convenient for illustrating the Oratory of the 
Feelings (English Composition and Rhetoric, p. 201). 

Self- Interest, — This comprises our pains and pleasures gene- 
rally (to the exclusion of our Sympathies), whether from sense, 
from emotion, or from the associated and comprehensive ends, 
as Wealth and Power. That men believe according to their 
self-interest hardly needs illustration. Not only does each 
man endeavour to deceive others, he generally succeeds in 
deceiving himself when his interests are at stake. We have 
all great difficulty in seeing the faults of an institution that 
we profit by ; the arguments of a highly paid priest for his 
own form of religion, or of a lawyer for lucrative forms of 
procedure, are regarded with suspicion. The grossest forms 
of error, the most noxious practices will be vindicated by per- 
sons whose worldy position depends upon them. 

Among the particular pleasures and pains making up the 
great aggregate of self-interest, we may signalize some as 
especially unfavourable to truth. Indolence, or the aversion to 
labour, the source of so many moral obliquities, is the parent of 
intellectual error. The ascertainment of truth demands a kind 
of labour that the average human being dreads and abhors 5 
hence the acquiesence in such views as come easiest to hand. 
That unqualified extension of the present to the distant, the 
past, and the future, w T hich we have seen to grow out of the 
inherent activity of the system, is still farther recommended 
by the saving of toil. Excessive identification, generalization, 
and simplication are other expressions for the same tendency ; 
while complication, and incoherent details, are preferred to a 
simplifying generalization that would cost great labour. 

One form of self-denial requisite for getting at truth is to 
withstand the influence of the present, and the palpable. A 
present impression has a commanding potency. The inherent 
tendency to assume that what is will be, is aggravated by any 
unusual impressiveness of the present fact. The first victory 
of a campaign elates the conquering army with confidence in 
the future. 

The Sympathies. — The sympathetic tendency of our nature 
while antagonizing self-interest, and the errors thereby induced, 



EXCESSIVE STMPJ 

is a source of errors peculiar to itself, 
in with the feelings and views of th 
opinions that have once < 
sometimes dependent for a move i 
an excessive egotist. 

The disposition to see as i 
fellow-beings has nursed various In 
it is said of errors, that they are almost 
truths; which maybe the ease with cert.: 
tainly not with all, probably not with the mi 
has usually some show of fact to res: up 
say that the ante-copernican doctrines of Asti 
half truths; that the sun and stars move round I 
was a total mistake. That despotic government i;; . 
happiness and the improvement of mankind doi 
to be called a half truth. It is the conversion of a 
ceptional instances into a general canon. 

Another fallacy of excessive sympathies is that v. 
been in the past has always been more or less suital 
time and circumstances. Thus, slavery, it is said, 
disapproved of now, was once necessary and Buitable. i 
cution for opinions was the fitting accompaniment o: 
state of civilization. Feudality and hereditary monarchy 
now cease to be essential, but were so in former time 
encomiums on the past need to be received with g 
givings. To justify them fully, we must maim . th.it 

the good of mankind has been the chief mol 
and supporters of the actual institutions of evi 
secondly, that men's ingenuity of contrn 
on a level with their necessities. We 
essential to human society that the G 
Pericles or of Xenophon should be 
happened to be taken in war ; such i 
induced to work by the motive of pay. 

The Special Emotions .—The qo\\> 
of the leading emotions will bring to view 
sources of fallacy arising from the feeli 
is still mainly due to their being pl< 
there is in emotion also the influ 
irrespective of pleasure, in occupy i: 
the trains of thought. 

We may remark first on the I 
generally, or, as it is also called, tl 
the effect of which is to dwell upon tl 



G12 FALLACIOUS TENDENCIES OF THE MIND. 

tiling Men endowed with this peculiarity over-estimate all 
tha^°is good in their prospects, and in the prospects of the 
world generally. They are optimists as regards both the 
present and the past. "They fall into the last named error — 
that whatever was, was right. Mere sympathy, without 
the Fanguine temperament, might not so readily fall into that 
mistake. The opposite temperament works in the opposite 
direction ; it is the source of disheartening views of things, 
and forebodings of disaster. The fluctuations of the mental 
tone in each individual have temporarily a like influence on 
the beliefs. 

The emotional temperament indulges in delightful ideal con- I 
ceptions, from which are excluded the stern features of the 
reality. Hence the fallacious picture of a beneficent despot— 
the blessings of absolute authority in good hands— which 
occupies the minds of sentimentalists, and plays into the 
hands of real oppressors. 

The emotions of Novelty and Wonder have been ofcen 
descanted on as sources of corruption. They disincline men 
to any facts, views, or theories, that have not in them a dash 
of the marvellous. It is difficult to get good observations on 
the mental faculties of the lower animals, from the wish to 
invest everything about them with mystery and wonder. The 
same cause preverts the records of travellers in foreign 
countries. Even physical phenomena that have anything 
marvellous abort them are difficult to observe with precision ; 
and the statements of unscientific persons are generally 
untrustworthy. The fondness of the human mind for exag- 
geration and hyperbole renders a great part of human speech 
untrue to fact. 

The Emotion of Fear, superadded to mere aversion or dis- 
liking, unhinges and debilitates the mind, disposing men to 
dark and dismal views of things, and fitting them to be the 
slaves of whoever has the power to terrify. Under the shape 
of Superstition, the susceptibility to fear has held mankind in 
captivity to innumerable delusions, especially in all that per- 
tains to the supernatural. As the enemy of science, supersti- 
tion is dwelt upon by Bacon with peculiar emphasis. 

The feelings of Love, tenderness, affection, amiability, which 
are distinct from sympathy proper, although always in some 
degree fused with it, are corrupters of the intellect, by creating 
a disposition favourable to whoever is loved; hence the parti- 
alities of affection and friendship, the incapability of seeing 
anything wrong in one's country, sect, or party. In the 



SELF.— PERSONAL DIGNITY.— JBSTHK3 I 

higher compounds, termed Admiration and R 
a still greater power to sway the judgment I 
Deference to great authorities, and to the prevailin ■ 
society, and the readiness to admit coruprom 
to the loving and sociable dispositions, Tb 
are easily led into the worship of antiquity, m 
mental stronghold of blind conservatism/ 

The emotions of Self— the special circle of \ 
ceit, Pride, Feeling of Dignity— in proportion t 
disturb the judgment of what is true. The 
own opinions, because they are ours, the plans, 
theories of our own concocting, the value set uj» 
that touches ourselves, — are snares in the way bo trul 
egotism even comprehends family, friends, party, an I 
to all of whom, as being related to ourselves, we attriba 
superior wisdom. National prejudice is one of tb 
structives of political progress. 

The sense of Personal Dignity operates to p 
in a remarkable degree. Many prevalent doctrini 
mended by their supposed contribution to the dignity ol ho 
nature. A leading argument in favour of the Immaterial 
the Mind or Soul is expressly grounded in th 
of the immaterial essence. The doctrine of Free-will is 
posed to elevate human nature by the ennobling function of 
autonomy, gelf-government, or judicial arbitr 
modern hypothesis of Development is objected to 
our ancestral pride. The exceeding sinfulness attributed 
human nature by the Calvinist would be highly nnp 
but for the tribute indirectly paid to our self- imports 

Our emotions of Anger, like Fear, are manil in- 

duced upon mere pain. Revenge, antipathy, hatred, | 
spirit, are forms of the irascible feeling, and 
in a conspicuous degree, to the ascertaining of truth. ( 
the expression of anger, connotes falseli 

We may conveniently group under the 
variety of emotional states, of which the central an 
mode is Artistic Harmony, but which in\ i many of tho 

other emotions — as Novelty, Won 
emotions aimed at in poetry and in 
a large mass of powerful feeling. M 
philosophy, and numerous petty ovv^u^ and per 
to be ascribed to this department of on 
bilities. Thus in the ancient world, the minds of phi 
were, dominated by the idea of symmetry, 



61-i FALLACIOUS TENDENICIES OF THE MIND 

and harmony. Pythagoras was entranced by the mystery of 
number ; Plato followed him ; and Aristotle was not exempt 
from the spell. P>ut the predominant source of fallacy quotable 
under the present head was the supposed Perfection, Dignity, 
and Bccomingness of certain arrangements in nature, which 
included numerical considerations among others. The superior 
worthiness of tire was declared in the Pythagorean philosophy ; 
and even in the later Copernican controversy an argument was 
founded on the circumstance that the new system placed fire, 
the noblest element, in the centre of the universe. So only 
Mind, according to Plato, in Philebus, is sufficiently dignified 
to create the world. In the recital by Socrates, in Phsedon, 
of the phages of his intellectual history, on the subject of Cause, 
the doctrines of Thales and Anaxagoras are set aside because 
they do not recognise the becoming as a power in the world. 
The adherence to the circular form of the planetary orbits, 
because of its perfection, was inveterate in the cool mind of 
Aristotle. The planets could be only six, because that was a 
perfect number. 

The dictation of a plan to Nature on a supposed propriety 
has run through all times. Even in hard business affairs of 
trade, Aristotle held it was against nature that money should 
breed money, that is, pay interest on loans. Lamarck argues 
that a Polype cannot have Sensibility, because it would be 
contrary to the plan that Nature is obliged to follgw in all her 
works (Lewes's Aristotle, p. 97). 

The fiction of Unity, which carried away the early Greek 
philosophers, partly proceeds from over-assimilation, and partly 
ministers to artistic emotion. The absolute unity of mind 
is still worshipped by German philosophers. Herbart and 
others, rather than admit the radically distinct nature of Feel- 
ing, Will, and Intellect, insist upon regarding Intellect or 
Cognition as the basis of the two others. 

The artistic sublime dictates such exaggerations as ' Let 
justice be done, though the world collapse ; ' ' Truth is great 
and all-prevailing. ' Only a mind driven off its calm centre 
by the sublime of Force can exclaim « Might is Right.' The 
fallacy that makes Artistic Harmony the test of truth, almost 
inevitable in poetry, is deliberately maintained in Wordsworth's 
Essay on Epitaphs, and in his prose criticisms. 

I he allegation is often made, on instances garbled to chime 
in with an amiable sentiment, that great men derive their 
mental power chiefly from their mothers. 

The influence of aesthetic qualities — beauty, sublimity, bar- 



INTELLECTUAL ASSOCIATIONS. 






mony, propriety— is constantly operating to twist tho u, 
standing The architecture, music, and colouring empl 
m religion, indispose the worshipper to canvass the valid.. 
the doctrines. Ihe art of the orator involv, 
the sense, and the charms of style. Such subjects as 
Criticism Morality, tho Human Mind, wher ,h £ 

more or less attended to, are liable to distortion through 
circumstance. Of Rhetorical devices, only a fe* . User- 

vient to truth ; while a great many aro hostile. 

The interests of Morality and Religion, have, in aln 
every age and country, been thought to require a babil 
exaggeration of the pleasures of virtue and the misers 
Plato was the first openly to recommend the pious 
preaching doctrines, in themselves false, as being favourable 
to morals and social order. And although only one sociel 
modern times-— the Jesuits— has formally avowed the 
principle, there has been a wide-spread disposition to put it in 
practice. Various apologists for Christianity have contended 
that, even supposing it untrue, it ought to be propagated on 
account of its beneficial consequences. 

III. Influence of Associations. 

Belief is not founded in the intellect; yet the intellectual 
associations confirm tendencies pre-existing, and contribute to 
belief both in the true and in the false. When two things have 
been often associated together in the mind, the impetus thus 
acquired, in passing from the one to the other, counts as a 
force of belief. We are disposed, by our inborn activity 
proceed upon whatever we are told, there being no counter- 
acting tendency present ; the frequent repetition of the same 
declaration enhances our disposition to believe it. Tho force 
of iteration is one of the leading causes of men's beliefs. What 
has often been said, and seldom or never contradicted, is all- 
powerful with the mass of mankind. 

Thus, one part of the influence of education, and of pre 
ing opinions, is due to an intellectual link, whose growth could 
be arrested by mere counter iteration. Tho same infloem 
at work confirming our modes of looking at things. There 
may be no reason, beyond the adhesion generated by lei 
of time, why a man is reluctant to entertain a new opinion, 
and yet this may be enough to render his conversion impr 
cable. It was remarked that Harvey's doctriue of tho circu- 
lation was admitted by no physician past forty. Am 
habits, we are to reckon beliefs* The inveteracy of | 
opinions is in great part due to their being long cherished. 

27 



CHAPTER IV. 



Fallacies of confusion. 

These fallacies cannot usually be produced as direct contra- 
ventions of logical method. Many of them depend on imper- 
fect acquaintance with the subjects under discussion. A 
certain number may be regarded as snares of language 
(Bacon's idola fori). A logical discipline is good as against 
many ; and their detailed exposure may have a slightly forti- 
fying influence. As already remarked, an exhaustive treat- 
ment is not possible ; but certain genera may be selected as 
being both prevalent and deleterious. 

Fallacies of Language. 

Ambiguous and ill-defined lerms. — The Fallacies of Equivoca- 1 
tion of the scholastic logic are fallacies of ambiguous langu-> 
age; for which the remedy is an exact definition of all 
leading terms, and an adherence to the meaning so settled, i 

It is one criterion of an advanced science to have its terms j 
defined. In subjects not raised to scientific precision, we may 
expect vagueness in the use of language. The Mathematical 
and the Physical Sciences were the first to make progress in 
this direction ; only in recent times has the progress been 
extended to the Moral Sciences — Psychology, Ethics, Politics, 
Law, Political Economy. 

The exemplification of ambiguous words has no limit, unless 
we adopt some principle of selection. For a work on Logic, 
the most appropriate examples are terms of leading importance 
whose ambiguity is still a cause of error and perversion. 

The word ' Nature ' is full of ambiguity. Butler pointed 
out three meanings. Sir Gr. C. Lewis, after a lengthened 
examination of particular uses of the word, found that they 
fall under two classes: — (1) A positive idea, as expressing 
essence, quality, or disposition ; (2) A negative idea as excluding 
art, or human regulation and contrivance. This last meaning 
occurs in the phrase state of nature, used to designate man's 
existence before the introduction of law, government, and the 
arts of civilization. As human interference may sometimes be 



AMBIGUITY OF 1 

good and sometimes bad, the meaning of na1 

ingly. When men's ' natural rightf 

great doubt as to what is intended. 4 Every nan 

right to his liberty ' — is a jumble of uncertain sound* ; 

being probably used in Lewis's second acceptation, ai 

antithesis of art, regulation, and interference 

'Liberty* has various meanings. It is not in. r« ivtli- 
of coercion or restraint, as being at large instead <>t being it 
soned ; it extends also to the possession of p 
status; thus in a community where there : i (pri- 

soned; it extends also to the possession of powei 
distinction, and freemen compose a privileged order oi I 

The ambiguities of 'Moral ' have been previously adv» 
to. Even in the one specific meaning of * rigiii and 
it has a fluctuating signification, and has given occasion to 
erroneous views. The criterion of 'moral' and ' imm< 
in the accurate meaning, is Law ; a moral act is imp 
superior ; hence a supreme power cannot do an immoral, any 
more than aa illegal act. When the Deity is said to hr.ve a 
'moral' nature, the word must be supposed to mean si 
'goodness/ or else 'equity,' both which qualities may a1 
to a supreme legislator; the sovereign power may do a 
chievous act, and may be guilty of partiality or nnfairaei 
between one man and another; which, however, is not the 
connotation of immoral or illegal, according to the pr 
definition of the terms. The sovereign has no moral du; 
his acts create these for his inferiors. 

The confusion of Law in the juridical sense, with L 
uniformity of nature, is exemplified in Butler's cbapfa 
Moral Government of God. Jiutler calls the ' ci Na- 

ture ' a government, merelv on the ground that it induces 
precautions to avoid pain. But these precautions 
moral in them; they may be used for criminal ends. I 
Fawkes most faithfully obeyed the laws of nature, 
placed his barrels of gunpowder so as to ensure the 
up of Parliament, while he arranged for firm- them 
to himself. It is the object of a Law proper to 
from injuring one another; the uniformity ot nature I 
itself equally to good and to evil condi; 

The word 'Utility' has a narrow sei 
elegance, and refinement ; and a wider b 

theory of Morals), comprehending (he whole ^man 

gratifications and well-being. 

' Self has several meanings, which have to be ng\ed 

in ethical reasonings. 



618 FALLACIES OF CONFUSION. 

The words ' same/ * identity/ have often been commentec 
on. Similarity or sameness is a matter of degree, and in this 
consideration alone lies the ambiguity. A human being h 
called the same person aU through life, although in man} 
respects changed. 

• Probability ' is not always used in its proper meaning 
ur.mely, the expression of what is true, not in every case, but ir 
most. Not unfrequently, the two sets of cases, pro and con, 
are called the probabilities for and against a thing. The 
wind blows from the east, say three days in seven, and from 
the west four days in seven ; the proper expression then is, 
there is a probability of four to three in favour of west wind 
on a given day. To say that the probabilities are four in 
favour of, and three against, a west wind leads to a confounding 
of the probable with the improbable. A vacillation between the 
meanings is observable in Butler's Introduction to his Ana- 
logy. He correctly expresses the nature of probability when 
he speaks of there being a greater presumption upon one side 
of a question than upon another, and remarks that if there be 
the slightest preponderance, prudence requires us to act; 
accordingly. He goes on, however, to say that, in questions 
of great consequence, we have to be content with probabilities 
even lower; that is, where there is an equal balance on both! 
sides ; nay, even to less than this ; in other words, we are to 
act with the majority of cases against ns, which is to believe 
in the improbable. 

The play of ambiguity is seen in the remark of Aristotle — 
4 That which is naturally good is good and pleasant to the good 
man / an equivocation too closely resembling what occurs in 
Plato's argument to show that the wrong-doer, if unpunished, 
is more miserable, than if he were punished. * The wrong-doer' • 
says Plato, * when punished suffers what is just ; but all jusV 
things are honourable ; therefore he suffers what is honourable. 1 
Now all honourable things are so called because they are either! 
agreeable, cr profitable, or both together. Punishment is not 
agreeable; it must therefore be profitable or good. Whence the 
wrong-doer when punished suffers whatis profitable or good, &c.' 

Separate meanings ascribed to separate words. — This is one of 
the greatest snares of language. There is a strong tendency 
in the mind to suppose that each word has a separate meaning, 
and to be misled by tautologies and alterations of phraseology. 
The ramifications of this tendency are numerous and subtle; 
they include the master fallacy of Realism, or the conversion 
of Abstractions into Realities. 



DUEAD OF CHANGES IN LANGUAGE. 

The strong verbal associations formed with nil our opinion! 
and views make us alarmed when it is propose! to with 
the customary phrases in favour even of such as are 
suitable. Srillingfleet complained that L >cke's docl 
cerning Ideas ' had almost discarded Substan< ; the 

world.' ^ This feeling has been manifested againsl all the 
innovations of philosophy. Because the Cartesian do 
Mind and Matter, as two distinct things, is declare 
gratuitous and destitute of proof, people are shocked as if 
Mind were done away with. The same revul- 
enced towards Berkeley's attempt to reconcile the couti 
tion of the prevailing mode of regarding Perception. Wl: 
disposes of Hume's objection to miracles 'as contrary to tho 
Course of Nature,' by the retort that, according to him, there 
is no such thing as a Course of Nature, there being nothing 
but ideas or impressions on the mind of the individual. 
unproducible entity 'Substance' is upheld in man's minds by 
the force of the word. 

The fallacy of the Identical Proposition is due to there being 
two different names for the same thing : — 

There's ne'er a villain dwelling in all Denmark. 
But he's an arrant knave. 
Ferrier complains of the phrase * Perception of Matter,' as a 
a duplication of words for one fact, leading people to suppose 
that there are two facts. So, between antecedent and conse- 
quent, in Causation, there is interposed the name 'power/ 
to which there is nothing corresponding ; the fact I- 
sufficiently stated by the uniform sequence of the antecedent 
and its consequences. 

There is a difficulty in satisfying men's minds that Resist- 
ance, Force, Inertia, Momentum, Matter, are all one fact. So 
with the terms Motion, Succession, Direction, Distance, Situa- 
tion, Extension — which are modifications of one fundamental 
fact — Movement and the possibility of movement, | 

The giving reality to Abstractions is the error of Realism 
and is not as yet fully conquered. Space and Time 
frequently viewed as separated from all the concrete experi- 
ences of the mind instead of being generalizations of 
certain aspects. Certain things are said to be 'out of all relation 
to Time,' which should mean that such things have 
cession and no endurance. ' Time as the innovator,' 
an unapt metaphor, or nonsense. So, 'Truth ' in the 
is a fiction; the reality is a number of true proportions. 
4 Chance ' lingers in men's minds as an independent existence, 



(520 FALLACIES OF COKFUSION. 

instead of an assertion of identity between certain concrete 
situations. 

The word ' Existence ' in its most abstract form refers to a 
supposed something attaching alike to the Object and to the 
Subject, over and above Quantity, Succession, and Co-existence, 
which are attributes common to both. The only meaning of 
the word is the Object together with the Subject ; for which 
addition we also employ the synonymous names, Universe, 
Being, Absolute, Totality of Things. To predicate existence 
of matter or mind is pure tautology. 4 Existence ' means 
matter or mind, or both, as the case may be. The only use of 
the word is to express Object or Subject indiscriminately, 
there being occasions when we do not need to specify either. 

The valuable distinction, struck out by Aristotle, of Poten- 
tial and Actual, is made the occasion of giving reality to 
fictions. The potentiality has no meaning but by a reference 
to actuality ; the power of moving means motion in given 
circumstances. ' Educability ' means education under certain 
conditions. Hamilton has created a fictitious intellectual 
faculty under the name " Conservative Faculty ;' a pure re- 
duplication of his * Reproductive Faculty/ We know nothing i 
of the conservation of thoughts, except that under certain 
circumstances they are recalled or reproduced. 

Unsuitable phraseology and unreal questions. — Many purely 
artificial perplexities have arisen from applying to a subject 
terms incongruous to its nature. The words ' true y and ' false ' 
are properly applicable to ku owl edge or affirmations respect- 
ing the order of the world ; they cannot be applied to pleasures 
and pains except by mere metaphor. A 4 false pleasure ' is an 
incongruous jumble, like a ' loud circle ' or a ' bright toothache.' 
Aristotle puts the question — ' Is happiness praiseworthy ?' — | 
to which there is no proper answer, because there is no proper 
meaning. 

The old puzzle respecting Motion is due to the improper use 
of language. Motion means ' change of place.' The puzzle is 
brought about by insisting that the phenomenon shall be 
expressed as in a place, that it shall be either in one place or 
in another. If we give way to this arbitrary restriction of 
language, we must allow, with Hamilton and many others, 
that Motion can be shown to be impossible. 

Allusion has already been made (p. 364) to the unsuitability 
of the word * hypothesis ' to express abstract notions, as the 
definitions of Geometry. 

The application of terms of Extension and Local Position 






FALLACIES OF SUlTRKSSID KKLATl VK. 

to the mind has been the source of factitious pu 

ficial mysteries. 'How the immaterial can b 

matter, how the unextended can apprehend extension, how 

the indivisible can measure the divided,— this is il . 

of mysteries to man' (Hamilton's lteid, p. b 

is, no attempt should be made to express the anion 

and matter in the language that would be suitable to the 

union of one extended thing with another. 

The most conspicuous example of an artificial difficulty 
created by incongruous language is the celebrated I 
theory. The sequences of the Wiliconsist of feelings follbl 
by actions; they exemplify mental causes giving birth to 
activity, and are broadly contrasted with the physical pi 
movers — as water and steam -which are devoid of any m 
element. There is no mystery in these peculiar Bequei 
except the mystery of the union of mind and body, formerly 
remarked on (p. 357). The introduction of the idea of J 
dom or Liberty into the voluntary operation is totally without 
relevance; and the consequence has been a seemingly insoluble 
problem, a mesh of inextricable contradictions, 

Fallacies of Relativity. — A large class of Fallacies consist in 
denying or' suppressing the correlatives of an admitted i 
According to Relativity, the simplest affirmation has two 
sides ; while complicated operations may involve unohvious 
correlates. Thus the daily rotation of the starry sphere is 
either a real motion of the stars, the earth being at rest, or an 
apparent motion caused by the earth's rotation. Plato m 
to have fallen into the confusion of supposing that both Bt 
and earth moved concurrently, which would have the ( 
of making the stars to appearance stationary. 

Every mode of stating the doctrine of innate ideas 
or borders upon, a Fallacy of Relativity, provided w 
the theory of Nominalism. A general notion is the affirma- 
tion of likeness among particular notions ; it, therefore, sub 
only in the particulars. It cannot precede them in the evolu- 
tion of the mind; it cannot arise from a 6ourco apart, 
then come into their embrace. A generality not embodied 
in particulars is a self-contradiction unless on & 
Realism. 

Kant's autonomy, or self-government of the will, is a fall 
of suppressed relative. No man is a law to hi: 
co-implicates a superior who gives the law, and an in!< -nor 
who obeys it; but the same person cannot bo both r. 
subject in the same department 



g22 FALLACIES OF CONFUSION. 

In Ethical questions there are examples of suppressed rela- 
tives. Thus, it is often set down as essential to the highest 
moral virtue, that law and obligation should embrace every 
act of human life, that the hand of authority should never be 
unfelt. Now, authority means operating by penalties, and 
appeals exclusively to the selfishness of men's nature. Uni- 
versal obligation is universal selfishness, which is not what is 
intended by the supporters of the doctrine. 

The view is sometimes expressed that the civil magistrate is 
bound to support (by public establishment) the true religion ; 
which, however, can mean only what he thinks the true reli- 
gion ; and the correlative or consequence is that he is bound 
to establish a false religion, provided he believes it to be the 
truth. This is an offshoot of the fallacy arising from the 
suppression of the subject mind in affirmations. An affirma- 
tion correlates with an affirmer ; a truth supposes a believer. 
(See Part First, p. 80). 

A Fallacy of Relativity is pointed out, by Mr. Venn, in the 
doctrine of Fatalism ; a doctrine implying that events, depend- 
ing upon human agency, will yet be equally brought to pass 
whether men try to oppose, or try to forward them. (Logic 
of Chance, p. 36G). 

The doctrine of Relativity is carried to a fallacious pitch, 
when applied to prove that there must be something absolute, 
because the Relative must suppose the non-Relative. If there 
be Relation, it is said, there must be something Un-related, 
or above all relation. But Relation cannot, in this way, be 
brought round on itself, except by a verbal juggle. Relation 
means that every conscious state has a correlative state ; which 
brings us at last to a couple (the subject-mind, and the object 
or extended world). This is the final end of all possible cogni- 
tion. We may view the two facts separately or together ; 
and we may call the conjunct view an Absolute (as Ferrier 
does), but this adds nothing to our knowledge. A self-con- 
tradiction is committed by inferring from 4 everything is 
relative/ that * something is non-relative.' 

Fallacies of Relativity often arise in the hyperboles of 
Rhetoric. In order to reconcile to their lot the more humble 
class of manual labourers, the rhetorician proclaims the dignity 
of all labour, without being conscious that if all labour is 
dignified, none is ; dignity supposes inferior grades ; a moun- 
tain height is abolished if all the surrounding plains are raised 
to the level of its highest peak. So, in spurring men to 
industry and perseverance, examples of distinguished success 



BEGGING THE QUESTION.— SHIPPING TIIK BOUND, 

are held up for universal imitation; while, in I-, 
owe their distinction to the general backwardni 

Petitio Principii. 

Petltio Principii, Petitio Qunesiti, arguing in a ijing 

the question— -are names for a fallacy always iucl 
logicians in the List of Fallacies. To assume Bom< 
the premises the very point to be proved is frequent i 
with ultimate truths. The attempts to prove causal 
uniformity of nature usually take it for granted in I 
or other. The inductive syllogism is a petitio principii 
another instance, suppose, on the one hand, the continnil 
motion were given as the proof of Persistence of F 
on the other baud, the Persistence of Force given as the | 
of the continuity of motion, the argument would revolve in a 
circle. 

A chemical writer (Gmelin) assigns as the cause of chemical 
decomposition by superadded bodies leading to new c 
pounds, that the forces tending towards the new comp -muds 
are stronger than those maintaining the old. 

Hamilton remarks that Plato, in Phaedon, demonstrates the 
immortality of the soul, from its simplicity, and in the 
public, demonstrates the simplicity from the immortality. 

Ignoratio Elcncla. 

Ignoratio Elenchi, shifting the ground, or answering to the 
wrong point, is committed in many controversies. An example 
is furijished in the controversy relating to a Moral Sense. 
The opponents of the doctrine urge as an argument agaioftl 
a primitive or intuitive moral standard, that different nations 
differ widely in their notions of what is right and w: 
The reply is, that although they differ in the substan 
moral code, they agree in holding some things to be right and 
morally obligatory. This, however, is shifting the ground. 
The reason for appealing to* an implanted sense of Right 
to obtain for certain moral precepts a higher authority than 
human convention could give It was not to prove us end 
with a sense that something or other is a moral obligation, but 
to establish the obligation of certain assigued rules (tho 
morality of our own time). 

In books on Practical Ethics, there is usually a chapter on 
'Our duties to ourselves.' Like the autonomy of the Will, this 
is a Fallacy of Relativity, being a contradiction of the I 
idea of duty, which implies a superior authority. The ditH- 



CHAPTER V. 



624 LOGICAL FALLACIES. 

culty is met by shifting the ground; the allegation being 
that the care of our person and our interests is a duty to 
society and to God. 

The * Fallacia accidentis ' and the ' a dicto secundum quid 1 
ad dictum simpliciter ' might be brought under ' shifting the 
ground.' The meaning of a term is changed in its application ; 
'water quenches thirst,' does not mean ' boiling water.' So, the 
pleasures of duty are not pleasures attaching to it as duty, or 
as self-sacrifice, they are incidental consequences of the situa- 
tion, through the reciprocal conduct of the other party. 

False Analogies. 

The irrelevant comparison, or unsuitable analogy, is a usual 
form of confused and erroneous thinking, especially in the 
older philosophy. It abounds in Plato (see especially Timasus) 
and is not unfrequent in Aristotle; it is also prevalent in 
Bacon's attempts at scientific investigation. 

A familiar but highly illustrative example is the comparison 
of the history of a nation to the life of man, in respect of birth, 
growth, maturity, and inevitable decay. The comparison is 
irrelevant ; the likeness palpably fails in the most important 
points. A nation's losses are repaired ; the physical failure 
of a human being is irreparable. 

The reply to all such comparisons is to indicate the failure 
of identity. They are false minor propositions ; and the false- 
hood is exposed by pointing out the dissimilarity of the subject 
with the subject of the major. They are of the same nature 
as a pleading in law where the relevance is nnsound. The 
remedy is found in hostile criticism. 



LOGICAL FALLACIES. 

> There may be advantage in providing a supplemental colleo 
tion of examples of Logical Fallacies properly so called, that is, 
violations of the prescribed Logical rules and methods; it being 
fully understood that the exemplification of the rales them- 
selves, in the regular exposition, unavoidably affords instan- 



ces of their neglect or failure. 



EQUIVALENCE, DEDUCTION, AND OTDUOTl 

The proper arrangement) of such an additional c 
(unless made promiscuous to test (ho ingenuity of th 
is the arrangement of the general Bubject. * Folio* 
order— Deduction, Induction, Definition 
with Deductive or Syllogistic Fallac 

Since, however, a separate department, | 
Syllogism, is made up of Equivalent Form 
mediate Inference, aud since mistakes mas 
this department (some of them the proper sou 
fallacies), the first clsss of Fallacies should be 
Equivalence, orof Immediate Inference. Th 
fallacies occur are the Opposition of Propositi 

The acutest minds have been snared by conform 
Contrary with the Contradictory, of Prop >sii 
reverse of wrong is right* should be 4 The rev- 
contains something that is either right or indiffe 
are objections against a vacuum ; but one ol them 
true : ' the guarded statement is, * if there be not a nniv 
plenum, there must be some unoccupied sp a.' 

The chief fallacy of Conversion is Simple Conversion <>f A : 
'all the geometrical axioms are self-evident; alt sell 
truths are axioms.' The connection of this mistake with tin) 
usual fallacies of syllogism, was sufficiently pointed out. 

The proper Deductive Fallacies are errors 
syllogistic forms and canons. They are mainly resumed in 
Undistributed Middle and Illicit Process, which i ially 

involve the simple conversion of A. But for the Miar 
language that leads to this inadvertence, a fallacy of syllo 
would be comparatively rare. 

The Inductive Fallacies include the most frequent and tho 
gravest of logical mistakes. Their exemplification \s 
naturally follow the expository order of the subject of In 
tion. We might commence with erroneous views of the nal 
of Cause, such as the suppression of important condit 
collocations. We might also connect with this part of tho 
subject the error of assigning more causes than a j> ! . 
menon needs. It is involved in the very idea of 00 
the effect is in exact accordance with tho cause ; bi 
the proof that more causes were operative th 
needed, defeats itself. If we have an adequate c 
slavery, or for the subjection of castes, or classes, in the I 
lovo of domination on the part of tho stronger, the ex: 
that tho state of society demands such an arrangement is of 
no value. This is the error called ' proving too much/ 



626 LOGICAL FALLACIES. 

Next are the Fallacies from insufficient employment or 
neglect of the Methods of Elimination. Under Agreement 
falls the mistake (exemplified in Medicine) of confounding 
induction with multiplication of instances, without variation 
of circumstances. Mr. Mill's Fallacies of non- observation 
likewise sin against the methods. An induction is not com- 
plete till all the instances, or representatives of them all, have 
been examined. Paley, in affirming ' that happiness is equally 
distributed through all classes of the community,' must have 
left out of account the larger part of the facts. 

The assertion that ' Species are never transmuted/ even 
although not disproved by positive instances to the contrary, 
would require an examination of facts far beyond what has 
ever been made. Leibnitz generalized his ' Law of Continuity ' 
from a few unquestionable instances, without verifying it 
through all nature. 

The fallacious inferences named c Non causa pro causa,' 
'Post hoc ergo propter hoc/ are fallacies of the inductive 
methods. Some circumstance coupled with an effect is held 
to be its cause, without due elimination. Thus, the luxury in 
the Roman empire is said to have been the cause of its down- 
fall ; commercial restrictions, in spite of which trade has 
prospered, are made the cause of prosperity. 

The fallacy of not recognizing Plurality of Causes will be 
apparent from what was advanced on that subject. So, the 
fallacy of trusting to the Inductive Methods in Intermixture 
of Effects was necessarily involved in the reasons given for 
coupling Deduction with Induction. 

Under Secondary Laws, there is obviously involved the 
fallacy of applying a general law to a concrete instance, or to 
an intermediate law, without the due modifications ; as if wo 
were to infer from the Law of Gravity that all the planets are 
falling direct to the sun. 

Fallacies of Explanation were expressly exemplified. A 
non-compliance with the logical conditions of Hypotheses 
would yield fallacies on that subject. 

Fallacies of Definition would, in the first place, express 
the use of ill-defined terras. Again, the failure to satisfy the 
methods and rules of Classification is a sin against Logic. 
We need but instance the wide prevalence of the error of 
Cn.ss-divisions. Bacon is prolific of divisions and sub-divisions, 
which are never logical. His four classes of Idola are not 
mutually exclusive ; his Prerogative Instances will be after- 
wards remarked on. 



APPENDIX. 

A,— CLASSIFICATION OF THE SCIENCES. 

It is here proposed to subjoin a short account of the different 
modes of classifying Science or Knowledge. The subjec 
various logical bearings. The concatenation of Knowledge u 
in itself a Logic. 

The mode of partitioning Knowledge that first gained atten- 
tion was Bacon's threefold division into History, Philosophy, 
and Poetry ; in correspondence with the three great modes 
of intellectual production, or faculties — Memory, Reason, and 
Imagination. History, the product of Memory, deals wit: 
dividual things ; Philosophy, the product of Reason, com] 
classifies, and works up these materials ; Poetry, the product of 
Imagination, is the department of fiction, fable, or creation, as 
opposed to the literal rendering of things in History and 
in Philosophy. 

In dividing and sub-dividing these leading departments, 
Bacon displays his usual copiousness. History is divided into 
Natural History and Civil History. Natural History is the col- 
lective matters of fact of the world, laid out under Cele 
Bodies, Meteors, the Earth, &c. Civil History isEcclesia.- 
Literary, Political, with minor sub-divisions. 

Philosophy refers to God, to Nature, and to Man. The first 
head gives Theology. The second is a somewhat crude sylla- 
bus of Mathematics, Natural Philosophy, and Metaph. 
The Philosophy of Man is divided and sub-divided in much 
curious detail, but with no logical precision. He spea!. 
man in a three-fold aspect— (1) Man in general, (2) the human 
body, and (3) the human mind. The theoretical and the | 
tical aspects of our knowledge respecting humanity are u 
criminately mixed. 

As a first attempt at partitioning the totality of Literature, 
the scheme of Bacon deserves to be commended. But the 
lines of demarcation are for the most part vague and oni 
factory. The distinction of Individual (as History) and ( I 
ral (as Philosophy) is wholly unsuited to a primary diri 



628 CLASSIFICATION OF THE SCIENCES. 

of knowledge ; we canuot divorce the particulars from th< 
generalities in the same subject matter. 






The main outline, as regards the three-fold Division, was 
maintained in the classification of D'Alembert, intended for the 
plan of the French 'Encylopedie'; but with great improvements 1 < 
in the sub-divisions. The sub-division of Philosophy, relating 
to Nature, is a methodical arrangement of the Mathematical, 
the Physical, and the Biological Sciences, together with the 
more Scientific Arts, as Medicine, Agriculture, and Metallurgy. 

The Natural History department of History includes Meteors, 
Geography, Minerals, Plants, and Animals, very much on the 
scheme of Bacon, with the curious detached addition (also 
after Bacon) of a division for Prodigies, or deviations from the 
usual course of Nature. 

The Science of Man is distributed under the two heads 
Logic and Morals. Logic comprises the arts of Thinking, 
Retention, or Memory, and Communication. Morals is General, 
that is, regards Virtue at large (Ethics) ; or Particular, — 
including Law or Jurisprudence. This is the mode of ap- 
proaching the science of mind that has been embodied in our 
Universities. Excepting in recently founded schools, there is I 
no chair for Psychology or the Theoretical Science of Mind ; 
the subject is left to come under Logic and Moral Philosophy ; 
the Intellectual Powers being described in the Logic course, 
the Active Powers in Moral Philosophy. 

Thus, in D'Alembert, as well as in Bacon, there is total 
confusion of the Theoretical and the Practical. 

The plan of subjects in the ' Encyclopedia Metropolitana,' ; 
(begun to be published in 1815), is worthy of being quoted. 
There are four Divisions in the work. 

The First Division includes PURE SCIENCES, divided 
into Formal— Grammar, Logic, Rhetoric, Mathematics, Meta- 
plrysics; and Real, Law, Morals, and. Theology. 

The Second Division is the MIXED SCIENCES,— Mechan- 
ics, Hydrostatics, Pneumatics, Optics, Astronomy [constituting 
the larger part of our usual course of Natural Philosophy]. 

The Third Division is the APPLIED SCIENCES, sub- 
divided into Experimental Philosophy — Magnetism, Electricity, 
Heat, Light, Chemistry, Acoustics, Meteorology, Geodesy ; 
Fine Arts ; Useful Arts ; Natural History (with applications 
to Medicine). 

These are the properly scientific divisions ; the other sub* 



NEIL ARNOTT.— AUGU8TE Co.Mii: M| 

jects are History, Biography, Geography, 1 
Miscellaneous information. 

The designations 'Pare,' * Mixed/ and 'Applied 1 
have characteristic meanings, although not pn 
out in the above scheme. The Pure S 
Abstract and Formal Sciences, not involving the 
of objects in the concrete ; the two Leading i 
Mathematics and Formal Logic. The Mixed 
the applications of the laws of the Formal 8 
things. The Applied Sciences, in so far as 
Mixed Sciences, should be equivalent to the Pracl 

Dr. Neil Arnott, in his work on ' Physics/ published in 
1823, gave wide publicity to a division more in harmony with 
our present views. He distributed the leading sciences under 
four heads, representing the four classes of general Lavi 
Nature — namely, Physics, Chemistry, Life, and M 
viewed Mathematics as preliminary and indispensable to the e, 
being the Science of Quantity, or Measure, but not a depart- 
ment of natural operations, in the same acceptation as Physics 
or Chemistry. All the sciences give foundation to Arts. 

In his subsequent treatise, entitled * Survey of Human 
Progress/ Dr. Arnott brought out more decisively the distinc- 
tion between Sciences and Arts, and between the Concrete and 
the Abstract Departments of Science. Concrete Science ho 
calls the knowledge of Things ; and he enumerates, under this 
head, Astronomy, Geography, Mineralogy, Geology, Botany, 
Zoology, the History of Man. Science, or Philosophy (Ab- 
stract), is the knowledge of Phenomena, and comprises the four 
fundamental departments — Physics, Chemistry, Biology, Mental 
Science. The Arts are classified as Mechanical, Chemical, 
Physiological, and Mental. 

The work of Auguste Comte, entitled * Cours de Philosophic 
Positive ' (1830-42), is both a classification of the sciences as a 
whole, and a minute sub-division of each, according to cl: 
fundamental principles. 

He first draws the primary distinction between the Abstract 
and the Concrete Sciences, which he fully illustrate*. The 
Abstract Sciences, being the fundamental or depart m- 
branches of Knowledge, are susceptible of an orderly classifica- 
tion on the principles of Generality, Simplicity, and Independ- 
ence. 

Accordingly, he commences with Mathematics, whose truths 



C30 CLASSIFICATION OF THE SCIENCES. 

are the most general of all, and wholly independent of the 
truths of any other science, while all other sciences depenc 
upon it. Its sub-divisions are, the more abstract portion called 
Number, including Arithmetic and Algebra, and the applica- 
tions of these to Space (Geometry), and to Motion (Rational 
Mechanics). 

His second science is Astronomy, which is the embodiment 
of the Law of Gravitation. It receives this position because 
the carrying out of gravity requires Mathematics alone, while 
the phenomenon of gravity is a prelude to Physics. 

Then come, in order, Physics, Chemistry, Biology, and 
Sociology, whose mutual position and interior arrangements 
are governed by the same ideas of growing dependence and 
complexity, and decreasing generality. 

In addition to the singling out of Astronomy as a leading 
science, Comte's arrangement has these two farther peculiari- 
ties, namely, the omission of Psychology, as a separate depart- 
mental science, (it being appended to Biology, nnder * Cerebral 
Functions/) and the inclusion of Sociology, or the Science of 
Society, as a fundamental department. 

Mr. Herbert Spencer, in his recent work entitled ' The 
Classification of the Sciences,' has criticised the scheme of 
Comte, and propounded one of his own, which he has devel- 
oped with circumstantial minuteness. He deals exclusively 
with the Theoretical sciences. 

Mr. Spencer's fundamental idea is the important distinction 
of Abstract and Concrete, which he expresses in a variety of 
forms ; it is the distinction between the Relations of pheno- 
mena and the Phenomena themselves, between the Analytical , 
and Synthetical ; it is the separation of one or a few sequences 
from the total plexus of sequences ; the wholly or partially 
ideal as contrasted with the real. 

Not content, however, with a simple binary division accord- 
ing to this leading contrast, Mr. Spencer proposes a three-fold 
division, by interpolating between the extremes a middle class 
partly Abstract and partly Concrete, to be termed Abstract- 
Concrete. The three classes are Abstract, Abstract-Concrete, 
and Concrete. The only way that this is competent is to sub- 
divide the Abstract, according to degrees of Abstractness. 
* Concrete r has no degrees ; it means the phenomena taken in 
their full totality, or individuality, — Stars, Mountains, Mine- 
rals, Plants, Animals; and there can be but one way of giving 
these totals, one mode of concreteness. There may, however, 



I 



HERBERT SPENCER'S CLASSIFI 

be various degrees of the analytic separation— more or lest 

abstract relations indicated ; quantity and 
Btracfc than weight, hardness, colour, life. 

The Abstract Sciences by pre-eminence, are those th.v 
with the most abstract of all relations- 
Wiohout affirming that Space and Time are intrinsically 
forms, conceived by us without any particular thi 
and enduring, Mr. Spencer holds that thoy have / this 

character by hereditary transmission, and that v. tuallj 

possess them in their empty condition, or apart from an? 
crete embodiments. Hence, whatever relations subsist with 
reference to these great conceptions, are the most absl 
the mind can possibly entertain ; they are pure and prop 
stractions; their hold of the concrete world lias been all 
if not altogether, severed. Space is the abstract of all 
tions of co-existence. Time is the abstract of all relations of 
sequence. Now there are two sciences that are occupied with 
these abstract relations of co-existence and of sequence— / 
and Mathematics; which accordingly form a class by them- 
selves, being removed from the next class by a wider int 
than separates the members of that class from one another. 

Proceeding from the blank Forms of existence, to Existences 
themselves, from the relations of phenomena, to the phenan 
we find two divisions, having different aspects, aims, and 
methods. In fact, we have the distinction of Abstract and 
Concrete carried out, without the same absolute divorce 
the previous class. Mr. Spencer illustrates the distinction 
thus: — Every phenomenon is a manifestation of force, usually 
a combination or complication of forces (the course of a pro- 
jectile depends upon at least three forces). We may study the 
forces either in separation, or in combination — the / 
the product. On the one hand, neglecting all the incideir 
special cases (say of falling bodies), we may aim at educing 
the laws of the common force (gravity) when it is uni 
fered with. On the other hand, given all the incidents of a 
phenomenon (as a river), we may seek to interpret the t 
phenomenon, as & product of the several forces simultaneously 
in action. The truths reached through the first kind of tn- 
quiry, though concrete inasmuch as they have actual i 
ences for their subject-matter, are abstract as referring to the 
modes of existence apart from one another. 

Mr. Spencer thinks it proper to point out farther that 
abstract must not be confounded with the yen mil. Each has 
its peculiar signification; 'abstract* means detachment I 



632 CLASSIFICATION OF THE SCIENCES. 

particulars ; ' general ' means manifestation in numerous casea. 
The law of uniform rectilineal motion is abstract ; but it is 
never realized in any particulars, consequently it is not gene- 
ral ; while rotation on an axis is very general. Accordingly, 
he disapproves of Comte's expression ' decreasing generality/ 
as belonging to the phenomena of the successive sciences 
— Mathematics, Physics, &c. This criticism indicates a point 
worth noting, but as regards Comte's remark it might easily 
be evaded. There can be no abstraction without a prior 
generalization ; the abstract law of rectilinear motion, is a 
generalization of the very highest order stating what would 
happen in every case when a body is projected into space and 
left to itself. The other kind of generality is something more 
special and concrete, in fact, much less of a generality than 
this great primary law. 

The Sciences, then, that treat of the forces of phenomena, as 
analyzed and handled in separation, are the Abstract- Concrete 
Sciences ; as Mechanics, Physics, Chemistry. The sciences 
that view phenomena in their aggregate, or their full actuality, 
are Concrete Sciences ; such are Astronomy, Geology, Biology, 
Psychology, Sociology, &c. 

A few words now as to the more precise definitions and 
divisions of the leading departments, on which hang various 
points of logical interest. 

Abstract Science considers, first, what is common to all 
Relations, and next, what is common to each order of Relations. 
Between each kind of phenomenon and certain other kinds of 
phenomena, there exist uniform relations. It is a universal 
abstract truth— that there is an unchanging order among 
things in Space and in Time. This is the most abstract truth 
of* all, the subject-matter of the highest division of Abstract 
Science. It has sub-divisions. First, and next in abstractness, 
are the connexions of things in Space and Time, irrespective 
of the things connected. This is the subject-matter of Logic, 
where the nature and amounts of terms related are not 
considered, but only the relations themselves. The other sub- 
division takes in Quantity or amount, without any farther 
qualities. This is Mathematics, which is a statement of laws of 
quantity apart from any real things, that is, as occupying 
Space and Time. This statement is made upon certain ultimate 
units occupying definite positions in Space and in Time. The 
divisions of Mathematics follow according as the units are 
simply separate, or according as they are both separate and 
equal ; the one gives birth to an indefinite Calculus (applied 






ABSTKACT AND CONCRETE SO] 

in Statistics), the other to the Defmito Calculc 

divisions are Arithmetic, Algebra, and i 

turns . When the computation of an q of 

Space, the subject is Geometry. When Time is u I, wo 

have Kinematics and the Geometry of Motion. 

So much for the sciences of pure Abstraction. The BbC 
class, the Abstract- Concrete, are occnpied with the l-< mem] 
laws of Motion, Matter, and Force, in their dil 
from the concrete phenomena, where they n 
modify one another. In Mechanics, for example, which 1 
of the sub-divisions, the laws of motion are expressed without 
reference to friction and resistance of the medium ( F 
Chemistry, another sub-division, the laws are view 
substances absolutely pure, such as Nature rarely Sftpplit 

The partition of this group is conducted on the same prin- 
ciple as in the former group. A distinction is drawn 1>< I 
Force considered apart from its modes, and Force cousin ■ 
vnder each of its modes, — a more abstract, and a 
department. The first part contains a statemont of the I 
of Force, as deducible from the fundamental principle 5l 
Persistence of Force, together with the theorems of the I 
position and Resolution of Forces. The second part comi 
Molar Mechanics or Molar Forces (Statics, Hydrostatics 
Dynamics, Hydrodynamics), and Molecular Mecha/iirs—\nc]u<\- 
ing the properties and states of matter (Physical), and Chi 
try; together with Heat, Light, Electricity, and Magnel 
[The arrangement is a questionable one, in so far 
is interposed between the Physical properties and 
bodies, and the agencies — named Heat, Light, A 

The division of Abstract-Concrete Science is thus « 
sive with what we have formerly termed Inorganic I 1 

The third great group, the Concrete Sciences, as n 
stated, embrace the totalities of phenomena, 
placed in this group. The meaning is, that tl 
does not stop short after generalizing the laws ot plan* 
movement, such as they would be if there ex- 
planet; he solves this abstract concrete problem 
wards solving the concrete problem of the planetary ini 
as affecting one another. The 'theory of I 
an interpretation of the Moon's motions, nut 
simply by centripetal and centrifugal fore,-, but 
modified by gravitation towards the Earth's eqt 
berance, towards the San, and even towards 
daily varvin" in their amounts and combinations, bo the 



634: CLASSIFICATION OF THE SCIENCES. 

geologist does not confine himself to the separate elements— 
water-action, fire-action, he aims to interpret the entire structure 
of the Earth's crust. And, in Biology, if different aspects of 
the phenomena of Life are investigated apart, they are all 
helping to work out a solution of vital phenomena in their 
entirety, both as displayed by individual organisms and by 
organisms at large. The interpretation is no longer syntheti- 
cal but analytical. 

These explanations premised, the enumeration of subjects in 
the Concrete division is as follows : — First, and most general 
of all, are the Universal Laws of the continuous Re-distribution 
of Matter and Motion. Next follows the application of these 
to actual Matter. As applied to the Celestial Bodies (1) treated 
as masses, it is Astronomy ; (*£) as made up of molecules — 
Astrogeny (Solar Mineralogy and Solar Meteorology). On the 
earth, the same actions result in Mineralogy, Meteorology, 
Geology ; when causing organic phenomena, they make up 
Biology, which has various sub-divisions, terminating in 
Psychology and Sociology. 

Such is the outline of Mr. Spencer's scheme. By way of 
criticism, the following remarks may be offered. 

In the first place, objection may be taken to bis language, 
in discussing the extreme Abstract Sciences, when he speaks 
of the empty forms therein considered. To call Space and 
Time empty forms, must mean that they can be thought of 
without any concrete embodiment whatsoever ; that one can 
think of Time, as a pure abstraction, without having in one's 
mind any concrete succession. Now, this doctrine is in the 
last degree questionable. For although we might concede the 
hereditary predisposition to fall into these conceptions, we do 
not thereby affirm that they can be bodied forth without any 
concrete examples whatever. We might rather say with 
Kant, and the later a priori schools, that when particulars are 
given they start forth into full view, This much is certain, 
however, that without a very wide and familiar converse with 
particulars, the exceedingly abstract relations of these Abstract 
Sciences, are wholly incomprehensible to any human being. 
The extreme generalities of Logic, in order to be intelligible, 
need perpetual reference to particulars. The same is true with 
the first elements of Mathematics, which are the foundations 
of all the rest. 

Mr. Spencer's account of the subject-matter of Logic, the 
first of all the sciences, is so extremely general that we can 
hardly discover what is the precise scope he assigns to it. 






LINES OF DL.MAL g^ 

From its position, however, it must be viewed u Tl 

Logic purely; under which there would be inclu 

mental aspects of all knowledge— Differem 

Agreement (Generality), the Laws of 

Inference, the Uniformity of nature ; and the t 

tions.or consequences of those primary facts. T 

common to all sciences, and may therefore p 

At the same time, it should be remarked that 

of these very high generalities has been a 

effort, considerably aided by the special 

mind, or the science of Psychology. This observation slightly 

qualifies Mr. Spencer's statement that none of the tl 

the third group are of any use to the problems of the .second, 

while the second group are of no use to the fii>t. 

It may be farther noticed that, notwithstanding the strong 
terms employed to contrast the Abstract with the Abfttract- 
Concrete Sciences, the contiguous subjects of each show but a 
narrow boundary line. The geometry of Motion, the last of 
the Abstract Sciences, comes very close upon the Univer 
Laws of Force, the first subject of the Abstract-Concrete -roup. 
These considerations, if they have any weight, tend to in- 
validate the alleged distinction between Abstract and Abstract- 
Concrete Sciences, a distinction without an adequate difference. 
Practically, however, the matter is of no moment. The sua 
fiion of subjects would probably be regarded as the .md 

the manner of sub-dividing and treating them would be very 
much the same with or without this particular boundary. 
Mathematics must precede Mechanics ; and Logic, conceived in 
its high theoretic aspects, may claim to precede Matheina* 
A much more serious dispute arises out of Mr. Spem 
proposed boundary line between the Abstract-Concrete and 
the Concrete Sciences. No one ever drew the lino as he has 
done it The Concrete Sciences have always Leen typified l>y 
the so-called Natural History Sciences — Mineralogy, Botany, 
Zoology, Geology — and by Geography. These are Scieootf 
whose marked features are Classification and Descripti 
They deal with large collections of objects, which they arrai. 
and describe by means of careful generalization. 

It is, therefore, with a little surprise that we find in>erted 
among Concrete Sciences, not merely Astronomy, but the 
whole of Biology, in which is included Psychology. Certaia 
parts of these subjects would be properly concrc 
Geography (under Astronomy; ; and the Races and Charac- 
ters of men (under Psychology.) 



C36 CLASSIFICATION OF THE SCIENCES. 

Let us consider how the case stands with Astronomy. This 
science, since Newton's time, is avowedly based on Theoretical 
Mechanics. Newton, in the First Book of the Principia, which 
may be pronounced Abstract Mechanics of the purest type, 
went far beyond Mr. Spencer's limits to an Abstract-Concrete 
Science. These limits, indeed, are not a little arbitrary. We 
can suppose a science to confine itself solely to the ' factors*/ or 
the separated elements, and never, on any occasion, to combine 
two into a composite third. This position is intelligible, and 
possibly defensible. For example, in Astronomy, the Law of 
Persistence of Motion in a straight line might be discussed in 
pure ideal separation ; and so, the Law of Gravity might be 
discussed in equally pure separation — both under the Abstract- 
Concrete department of Mechanics. It might then be reserved 
to a concrete department to unite these in the explanation of a 
projectile or of a planet. Such, however, is not Mr. Spencer's 
boundary line. He allows Theoretical Mechanics to make this 
particular combination, and to arrive at the laws of planetary 
movement, in the case of a single planet. What he does not 
allow is, to proceed to the case of two planets, mutually dis- 
turbing one another, or a planet and a satellite, commonly 
called the ' problem of the Three Bodies/ This problem is 
not to be touched in Theoretical Mechanics, but to be remanded 
to the Concrete Science of Astronomy. Yet, if we are allowed 
to combine the two factors— projectile motion and gravity to 
one centre — why may we not take in an additional factor, a 
second gravitating body ? The difference is not between 
single factors and their combination, but between two grades of 
combination. 

In point of fact, such a line is never drawn. Newton, in the 
First Book of the Principia, took up the problem of the 
Three Bodies, as applied to the Moon, and worked it to ex- 
haustion. So writers on Theoretical Mechanics continue to 
include the Three Bodies, Precession, and the Tides. Nor is 
any reason apparent for making the break that Mr. Spencer 
suggests. Increasing complicacy of deduction and calculation 
attends the inclusion of new factors, but this special difficulty 
is not supposed to take the subject out of an abstract depart- 
ment and to insert it in some concrete department. 

► Again, Mr. Spencer remarks that in works on Mechanics, 
the laws of motion are expressed without reference to friction 
and resistance of the medium. Turning to 'Thomson and 
Tait's Mechanics/ we find the Laws of Friction introduced, 
with a reservation of the purely Experimental results to the 



CHEMISTRY AND BIOLOGY. 






department called Properties of Matter. In 
Book, and m all works of .similar compass, Uio 
Resisting Medium is handled. 

The law of the radiation of light (the inverse tqoj 
distance) is said by Mr. Sp< 

while the disturbing changes in the modi am are u 
be mentioned except in a Concrete Scienc 
need not remark that such a separate handl 
science. 

Mr. Spencer's illustrations from Chemistry are v at 

variance w^ith usage, while it is difficult t 
with reason. Chemistry is .an Abstract-Concrete 
What does this mean ? The reply is, the chemist is i 
satisfied with the crnde substances of nature, but first pu 
them, and ascertains the properties in the pure state. Ti 
course* is a necessary precaution. Bnt if the insinuation be, 
that Chemistry does not give, or ought not to giro, th.- 
perties of any impure substance, or any alloy or mi 
the fact i3 quite different. Every chemical writer describes all 
the prevailing species of carbon, including pure and impure 
kinds ; the same with iron, and with every substance found in 
important varieties. Why should it be otherwise ? There 
dereliction of logical principles in stating the properties of 
the iron ores, in connexion with iron. The same thing mny be 
repeated in Mineralogy, but is not out of place in Chem 
Again, no writer on Chemistry ever omits to describe the 
Atmosphere, which is the actual or concrete combination of 
Oxygen, Nitrogen, &c. 

It may be noticed in addition that a substance pit 
obviously not a substance in the abstract. Virgin gold, 
the purest diamond are still objects in the concrete. 

These remarks on Chemistry pave the way for the 
ration of the place assigned to Biology among the 
Sciences. Now, Biology is a science of increasing coib| 
tion ; living bodies are subjected to all the I 
Chemical Laws, and to Biological Laws in addition : 
rose is a more complicated object than a diamond. Bat the 
objects of Chemistry and the objects of Biology ar 
concrete, so far as they go; the simple bodies of chert 
and their several compounds, are viewed by the Chem 
concrete wholes, and are described by him, not with reference 
to one factor, but to all their factors. * The isolation of th 
property, named Chemical combination, which would 1 
abstract handling of bodies in the chemical point of vieve, 



C38 CLASSIFICATION OF THE SCIENCES 

must be considered to be impracticable; at all events it is 
never done. We may doubt whether anything would be gained 
by attempting it. But, whatever abstractive operation of this 
kind is possible in Chemistry, might be repeated in Biology ; 
there might be general laws — isolated factors — of life, as well 
as of inorganic matter. If so, to place one of these two leading 
departments among Abstract Concrete Sciences, and the other 
among the proper Concrete departments is to make a dis- 
tinction without a sufficient difference. 

"Nor is it possible to justify the placing of Psychology wholly 
among Concrete Sciences. It is a highly analytic science, as 
Mr. Spencer thoroughly knows. The totality of mind is sepa- 
rated into factors, each discussed in isolation, before they are 
brought together. There are many strictly abstract discussions 
to show the difference between the effect of a motive (as selfish- 
ness) acting in ideal purity or separation, and the same motive, 
combined with many others, in the concrete human being. 
But the force of the remark would appear to be dissipated if 
all the laws of Psychology are to be considered as expressions 
of the concrete facts of mind. 

A separation may be temporarily made between the purely 
theoretical and deductive treatment of a science, and the ex- 
perimental treatment. In Theoretical Mechanics, (as Hydro- 
Dj^namics), the laws of a resisting medium may be inferred 
and computed from primary assumptions as to the nature of 
fluid particles ; while, on the other hand, the subject may be 
investigated by experiments, as in gunnery. But the science 
is not completely presented unless both are taken account of 
together : the theoretical deductions have to be confronted, 
checked and verified, by the experimental results, in order to 
have any standing as laws of the department. 

Tet another method is possible. A subject, as, for example, 
Astronomy, may be exhaustively handled in a separate treatise ; 
wherein there shall be brought together from every department 
whatever bears upon the celestial bodies. This would be a 
highly mixed department, yet not, on that account, a strictly 
concrete science. It would be full of the most abstract discus- 
sions ; witness the * Mechanique Celeste ' of Laplace. It would 
draw contributions from various sciences, besides its parent 
science, Mechanics ; it would introduce Optics, Heat, Magnet- 
ism, and Chemistry ; yet it would not treat the heavenly 
bodies as Minerals are treated in Mineralogy, or Plants in 
Botany. It would have many practical bearings ; in fact* it 
would have considerable claims to be a Practical Science. Any 



PRETENSIONS OF FORMAL LOGIC. 

•cientifie department exhaustively treated would eschew puritr 
and draw contributions from many sour Jf 

Thus, it appears that Mr. Spencer, in abandoning tho uiual 
partition of the sciences, into the departmental or fundamental 
sciences, on the one hand, and the concrete or derived on the 
other, has abandoned the more real distinction 
fanciful and untenable boundary line of tho Abstract and the 
Concrete. We see reason still to abide by the old sp. 
of the Concrete Sciences, typiGed by Minert 
Zoology, Geology, &c. These sciences have marks V 
themselves ; they are the dastificatory and the 
sciences. They embrace large collections of individual tb 
which have to be classified, and to be described a- 
wholes. Moreover, they contain no new fundamental ope 
of nature; every variety of natural agent has been pieri 
exhausted in the departmental sciences — Mathematics, Phi 
Chemistry, Biology, Psychology. 

B. — THE PROVINCE OF LOGIC. 

It is contended by some logicians that the Province of Logio 
is Formal Reasoning and Thinking ; by which they mean 
mainly the Syllogism, and what is subsidiary thereto. They 
would exclude everything that refers to the Matter, that is to 
say — Induction, and the greater part of Definition and Classifi- 
cation. 

We have, however, just grounds to complain that the dis- 
tinction of Form and Matter is too vague and unsteady to con- 
stitute a clear line of demarcation between the two departments 
of Evidence — Deductive and Inductive. It will be espc 
for us, therefore, to ascertain what precise meanings, if any, 
can be assigned to these phrases. 

Perhaps the most thorough and consecutive account of the 
severance of Formal Logic from [Material Logic is that con- 
tained in the Introduction to Mansel's edition of Aldrich. In 
that work, the author adduces every consideration that if of 
any avail in widening the distinction in question. 

Adverting to the first question raised in tho definition of 
Logic, namely, whether it be a Science or an Art — wheth 
is principally theoretical or principally practical— Mr. Mantel 
holds that, in its essence, it is speculative or th> and, 

in its accidents, practical. There would be a body of prin- 
ciples or laws, although no one cared to apply them to the 
discipline of the mind, or to the improvement of the thiukmg 
faculties. 

28 



640 THE PROVINCE OF LOGIC. 

Nevertheless, the science is susceptible of application tc 
practice ; it may be brought to bear on our intellectual pro- 
cesses. Such is its scope as expressed in the second part oi 
Whately's definition —the Art of Reasoning ; which definition, 
however, as regards the word * Reasoning/ Mr. Mansel, iD 
common with Hamilton and Mill, objects to as narrowing the 
province too much. Even as a Formal Science, Logic in- 
cludes the processes named Apprehension and Judgment, and 
these not as mere aids to Reasoning, but as independent acts 
of thought. Accordingly, Mansel agrees with Hamilton in 
substituting for ' Reasoning,' with suitable qualifications, the 
larger term 5 Thought.' 

He then proceeds to lay out the distinction between the 
Form and the Matter of the thought. His first indication of 
the difference is to this effect: — Thought may violate its own laics, 
and so destroy itself; something may be set up that turns out 
wholly unthinkable. On the other hand, a Thought may be per- 
fectly consistent with itself, but at variance with facts of 
experience; which, although quite thinkable, would be empiri- 
cally illegitimate, or unreal. [This is the distinction between i 
Self-Consistency — Immediate or Equivalent statements, and 
Inductive or matter-of-fact certainty]. 

The next remark is that there must be material data in order 
to thought of any kind, even formal thought ; there must be 
concrete experience of things external and things internal, in 
order to understand even a syllogism. But the materials being 
eriven, there is a vital difference between two modes of using 
.them. The distinction ofPresentative and Representative thought 
is an aid here ; the distinction between the individual concrete 
things — a building, a man, a star, and the generalities or con- 
cepts — height, figure, brightness, which we may form by the 
comparison of the concrete objects. The consideration of the 
Matter is the reference to the individual things ; the considera- 
tion of the Form is the general concept, or representative 
thought. [So far we have the ordinary distinction between 
Concrete and Abstract, only it is apparently pushed to a kind 
"of Conceptualism ; there being implied that the concept, or 
notion, is something more than an agreement among individuals. 
If it be true that a notion is unthinkable, except as one or 
more individuals, the 'Form' is still ' Matter,' only in a some- 
what different arrangement]. 

But farther, the thinking process may be distinguished as 
material or formal. It is formal when the matter given is 
sufficient for the product derived, with no- other addition but 



FORMAL THINKING EXPLAINED. 

be act of thinking. It is material wlien tho data are in 
cient, and the mind lias to take in more matter, m fcho i 
thinking. _ Given the attributes, A, B, (\ we can think 
as*co-existing in an object, without any fresh appeal to t 
which is formal conceiving. [This is quite intelligible 
the operations of Arithmetic are formal in this 6< 
nonnce six times four to be twenty lour, without an sppe 
pebbles or coins, or any real objects. We have put 
from primary realities a machinery that can operate independ- 
ently of the realities]. 

As conditions of formal conceiving, are laid down the laws 
of Contradiction and Identity. We must not introduce Con- 
tradictory attributes — A and not-A. The author is a little 
more obscure as regards the condition of Identity. Thought, 
he says, is representative of all possible objects ; but lutuition 
(cognition of the individual, as opposed to Thought, or the 
general) must be conscious of differences; every object of 
intuition is marked off, limited, and individualized ; it is its>lf 
and no other. To this circumstance corresponds the Law of 
Identity, ' A is A ' ; 'every object of thought is conceived as 
itself.' A somewhat novel rendering of that well-known Law 
of Thought. 

These laws are the key to logical conceiving (Conception is 
the first logical product). Next, as to formal judging, or the 
forming of Judgments. Affirmation takes place when one 
concept is contained in another; Negation, when one contra- 
dicts another. Here, too, are involved the laws of Identity 
and Contradiction. 

Finally, as to reasoning. This is formal when the given 
judgments are connected by a middle term, under such condi- 
tions of quantity and quality that the mere act of thought 
necessarily elicits the conclusion. If there be required any 
addition to the data, the consequence is material. Formal 
Mediate reasoning, no less than Immediate inference, is achieved 
through the laws of Identity (for affirmative syllogisms), and 
of Contradiction (for negative syllogisms). In the immediate 
inferences of Opposition [ObversionJ and Conversion, there is 
a further demand for the subordinate law of Exclude*! Middle. 

Thus, then, if a thought professes to be based on iormal 
grounds, to be guaranteed by the laws of thought alone, its 
preteusions can be adjudicated on by Logic ; if it pr< 
rest on sensible experience, or on suppressed premi.-es, it imi>t 
come before another tribunal. 

It is, of course, open, the author remarks, for any innovator 



0±2 THE PROVINCE OF LOGia 

to propose an extension of boundaries, by the inclusion of the 
Matter of propositions ; but he does so in the teeth of Kant's 
demonstration, that a criterion of material truth is not only 
impossible, but self -contradictory. Moreover, the attempt* tc 
enlarge the field renders impossible the assigning of any definite 
field whatever. 

We are interested to know in what way Mr, Mansel makes 
good these very strong allegations. The steps are these. 

(1) The Aristotelian or Formal Logic seeks the laws whereby 
the mind thinks; the Baconian seeks the laws whereby the 
phenomena of outward things take place ; that is to say the one 
refers to mind, the ego, the other to matter, the object, or non- 
ego. Consequently, the one enquiry is the interrogation of 
self-consciousness, the other is an examination of external 
nature. 

Such is Mr. Hansel's first position. It seems to involve some 
confusion of ideas. We strongly doubt whether the contrast of 
Formal Logic and Inductive Logic can be reduced under the 
contrast of Subject and Object, or Mind and Matter. 

For one thing, the study of Mind, or Psychology, is, in 
modern times, universally considered to be properly Inductive. 
How can we reach the important laws of Mind — such as Rela- 
tivity, Association of Ideas, the operation of the Feelings, and 
the Will — except by observation and induction of the facts of 
self-consciousness, occasionally aided by external indications. 

Again, the laws of Thought, called Identity, Contradiction, 
and Excluded Middle, apply alike to the outer world and to 
the mind. If so, they may be gathered from either source. 
Probably, however, the supposition is that these laws are got , 
at without investigation ; that they work themselves out with- 
out being expressly studied. We unconsciously and irresistibly 
declare that the same thing is not at the same instant white 
and black ; just as we walk without thinking how we walk. 

These invincible tendencies of the mind, if such there be, are 
no doubt facts of our mental nature : but so is our belief that 
Nature is uniform, or that every effect must have a cause ; on 
which reposes all Inductive investigation. In both cases, the 
mind is the instrument, although the material may be some- 
times mental phenomena and sometimes phenomena of the 
outer world. Deduction and Induction have equally their seat 
in laws of the thinking mind ; and have equally, for their 
field of operation, both mind and matter. 

(2) The next position is this — The Aristotelian laws are laws 
of thought as it ought to be ; the Baconian laws are laws of 






hansel's arguments. 



nature as it u. The author adds, as explanatory and 
ou8 statements, what seems to involve a new and dihtinol 
namely, that the one rest on their own evidence, the other 00 
the evidence of the facts concerned. 

To this we may reply that 'thought as it ought to ho' is 
certainly not couhued to Formal Reasoning. Wherever mt 
think wrong, and have to he put right, we°are in the domain 
of 'thought as it ought to be/ Lord Bacon's inductive logic 
professed to substitute right thinking for wrong. We commit 
fallacies of Deduction and of Induction equally ; and it bogie 
does not put us right upon both, it must be for some otbei 
son than the one now assigned. 

The addendum given, professedly to explain the above posi- 
tion, namely — that the Aristotelian laws are self-evident, and 
irreversible in thought, while the Baconian laws are inductions 
from facts and contingent or reversible — is merely a re-state- 
ment of the general thesis as between self-evident or nece 
truth, and inductive or contingent truth. 

(3) The third position is that th'3 Aristotelian Logic pro- 
ceeds from the law to the facts, constructing types or genera- 
lities, and rejecting what does not conform thereto; while in 
the Baconian Logic, the procedure is from the facts to the Into, 
rejecting every law that does not account for the facts. This 
is a direct opposition of Method. 

Now, we may readily grant this position. But what is its 
bearing on the question in dispute P The methods are different, 
but both are methods of arriving at truth ; both may be alike 
in want of precautions, and if so, both may, so far as appears, 
equally receive attention from the logician. 

(4) The fourth position is perhaps the most remarkable. 
It is this : Law, in the Aristotelian system, implies a conscious- 
ness of obligation; whereas, in the Baconian system, Law 
means only uniform sequence. 

Here is that confusion of thought, so well pointed out by 
John Austin, in connexion with the term ' Law,' when -by 
there is introduced into the order of natural phenomena the 
notion of authority and obedience. Law, as regards the order 
of nature, whether in mind or matter, is purely figurative ; it 
is applicable merely as expressing uniformity of ; the 

Ethical and Political definition— a rule set by intelligent 
superiors to intelligent inferiors, accompanied by the infliction 
of pain on neglect — cannot be transferred to the sequent 
nature, whether mental or material; the application to these 
contains only the single incident of law — uniformity. There 



Q±± THE PROVINCE OF L001C. 

can be no moral right or wrong in Logic, except only in so far 
as we are all morally bound to seek the truth, an obligation 
extending equally to truth Deductive and to truth Inductive. 

(o) A fifth position maintained by the author is, that, in the 
field of Thought, the cause is the conscious self; the effects, the 
thoughts produced by that self, through its own power, and 
under its own laws. To which we may reply, that both causes 
and effects are equally self, equally mental, but not thereby 
radically contrasted, in manner of investigation, with external 
nature. Cause and effect in mind must be discovered induct- 
ively, if at all. Should the sequences be very prominent, little 
attention may suffice for their discovery ; but that does not 
alter the method of proceeding. 

So much is Mr. Mansel carried away by the application of 
the term Law. in its Ethical sense, to the process of thinking, 
that he censures Mr. Mill for applying ' physical causation ' 
(meaning uniformity of sequence, ascertained by induction) to 
the moral and intellectual world ; as if there ever was any 
other mode of discovering the facts and laws of mind than the 
same processes, observation, and generalization, that apply to 
the material world. In short, he brings us round by a series 
of verbal ambiguities to the question of Free- Will and Neces- 
sity, which becomes thus a principal turning-point of the 
controversy as to whether Logic should, or should not, be 
confined to Deduction. 

The combined force of these five positions does not appear 
to establish either of the two allegations, namely (1) that a 
criterion of material truth is not only impossible, but self- 
contradictory, or (2) that to enlarge the field of Logic, is to 
assign it no definite field. We shall not here attempt a direct 
reply to the first, inasmuch as the exact basis of inductive 
truth will be fully considered in another place. (Appendix D.) 
The second allegation is a challenge to assign a definite boun- 
dary to Logic, while over-stepping the limits of the Formal 
Logic. 

Mr. Mansel puts so much more stress on the Theoretical 
than on the Practical side of Logic, that he would not be satis- 
fied with a reply based on the practical side. Let us enquire, 
then, whether a Theoretical Logic, embracing Induction, could 
be laid out and so circumscribed as not to be confused with 
any other scientific department, such, for example, as Mathe- 
matics, Physics, or Psychology. 

In the Introduction, we have indicated a field of Theoretical 
Logic, according to the larger meaning of the Province ; and 



SCOPE OF THEORETICAL LOGIC. 

in Appendix A, wo have given Mr. Spencer's survey of IU 
field m the same larger meaning. In summary, 
the topics. 

I. The Laws of Consistency, or Eqniraleoc 
commonly understood as the Laws of Thought J 
necessary (in the sense of analytic) infer 

give, in the view of Hamilton and Mansel, th. 
Syllogism. 

II. The Laws of Deductive or Mediate Inferer 
uented by the Dictum de omni et mdlo. This \ 

more than mere Self-consistency, or Equivalence. It might be 
called Mediate Consistency, the consistency of a conclusioc 
two conjoint premises, as contrasted with the c 
an equivalent transmutation of a single proposition. lift 
Mansel would hold that this consistency is necessitated and 
self-evident; and such an impression is not uncommon with 
thinkers generally. In opposition to that view, we I 
tended that nothing less than the induction of material in- 
stances would justify the conclusion. 

III. The Law of the Uniformity of Nature, which k 
basis of all material truth, and of all induction; consequently 
the basis of the syllogistic axiom of mediate consistency. The 
consideration of this law may well precede the ordinary 

for it is an assumption running through them all. It may, I 
fore, receive its first announcement in the science that 
with the criteria of all truth, namely, the separate scien< 
Logic. It is followed out into a series of formula*, known as 
the Inductive Canons, which, in their own sphere, may be 
pared with the syllogistic forms, in the Deductive Bpl 

Now, it seems to us, that a science may be construe 
to include the Laws and Formula? of Immediate 
Mediate Consistency, and General Uniformity, without t 
gressing the sphere of any other science. It need not run into 
Mathematics, the kindred Formal Science; it need n< • 
on the Physical Sciences, merely because it consider.- 
tulate necessary to them all, that is, Uniformity; it need not 
run into Psychology, although it derives from that bc 
explanation of the ultimate nature of Knowledge, as \)\i\\. 
and Agreement. And there does not appear to 
conterminous region. 

But we cannot concede to Mr. Mansel that L 
tially, or in the main, a theoretical science, and only ind 
ally practical. We contend that the science would never lrue 
been called into existence, but for its supposed practical utdity. 



64:6 THE PROVINCE OF LOGIG. 



i. 



Indeed, the same might be said of its splendid giant brother, 
Mathematics. However agreeable and recreative to some 
minds may be the contemplation of this great creation of ages, 
yet, but for the necessities and difficulties of measurement, it 
would never have been heard of. Mr. Mansel supposes a race 
of intelligent beings, subject to the same laws of thought as 
we are now, but incapable of transgressing these laws ; and 
declares that in the presence of such a race, the Logic of the 
Formal Concept, Judgment, and Syllogism, would remain the 
same. Unfortunately even for the illustration, there is a 
fallacy of Relativity in the very statement of the case. To a 
being that never committed an error, truth and error would 
be alike unmeaning ; to appreciate the valid moods of the 
syllogism, as contrasted with the invalid, such a being would 
have first to be told of an erring race, capable of confounding 
the two. Only after Adam fell did he know good and evil ; 
only by committing fallacies is any one competent to under- 
stand Logic. 

Postponing for a little the enquiry into the practical utility 
of the Inductive extensions of Logic, we shall advert more 
particularly to the distinction of Form and Matter, on which 
so much stress is laid in the present dispute. To some Formal 
Logicians the distinction does not appear in all respects satis- 
factory. Thus, Dr. Thomson (Outline of the Laws of Thought, 
§ 15) remarks : — 4 The philosophic value of the terms matter 
and form is greatly reduced by the confusion which seems in- 
variably to follow their extensive use. Whilst one writer ex- 
plains form as ? the mode of knowing ' an object, another puts 
it for ' distinctive part,' which has to do with the being or 
nature of the thing rather than with our knowledge of it ; 
where it means 'shape' in one place, which is often a mere 
accident, in another it means * essence ;' so that it may be 
brought to stand for nearly opposite things. I will add, that 
probably there is no idea which these terms represent that 
cannot be conveniently expressed by others, less open to con- 
fusion.' 

Mr. De Morgan says: — 'When it shall be clearly pointed 
out, by definite precept and sufficiently copious example, what 
the logicians really mean by the distinction of form and matter, 
I may be able to deal with the question more definitely than 
I can do at this time.' (Cambridge Transactions, vol. X. Part 
II. p. 8.) Again, ■ The truth is, the mathematician as yet, is 
the only consistent handler sf the distinction, about which, 



FORM AND MATTEH. 

nevertheless, he thinks very little. The diatinc form 

and matter is more in the theory of the loj 
practice; more m the practice of the math M l(1 

his theory/ ( Syllabus, p. 48). 

Hamilton illnstrates Formal Truth in Matben i» :— 

4 To the notions of Space and Time, 

existence of matter is indilTerent If matter had no existence, 
nay, if space and time existed only in our mind. 
would be still true; but their truth would bo of a pn 
formal or ideal character,— would furnish us with no ki 
ledge of objective realities/ (Logic II, p. o'G). But, in an 
place, he quotes, with approbation, from Essor, a pas>a 
the effect that truth consists not in any absolute hi 
thought, bnt in the correspondence of our thoughts with 
objects. * The distinction of formal and material truth is thus 
not only unsound in itself, but opposed to the notion of truth 
nniversally held, and embodied in all languages.' (Logic I. 
106). And again (Reid's works, p. 0^7), he remar. 
Reid's criticism on the Predicables, that Reid, like our British 
philosophers in general, was unaware of the difference 
the Logical or Formal, and the Metaphysical or Ileal. Tiio 
Predicables are forms or modes of predication, and not / 
predicated : in the langnage of the schools, second notions, not 
first.' 

Let us adopt Mr. de Morgan's suggestion, and refer to 
Mathematics for examples of Form, in the opposition to Matter. 
In so doing, however, we are merely taking up an old su 
under a new name. In Mathematics, we have the most com- 
plete development of reasoning by Symbols, called also AL 
reasoning. There will be other opportunities for exam 
the special processes of Mathematics (Logic or TH1 B 
Mathematics). For the present, let us note what bears upon 
the question before us. The abstractions of Mathematics, like 
all other abstractions, are embodied in concrete instances ; the 
Form is always given in some kind of Matter. Dut the 
matter needed is so very spare and attenuated, that, by a 
stretch of language, we may say it is no matter at all. 
the circles of Euclid are circles of printer's ink ; they have 
colour and a definite size. If we compare them with the 
round shield of Achilles, or a gorgeous centre ornament in the 
roof of a palace, we may describe them as void of matter and 
substance ; but they have their own substance, nevertheless. 

The symbols of Arithmetic (still more, of Algebra) are 
material, although their peculiar shape has nothi: i ula- 



64:8 THE PROVINCE OF LOGIC. 

tive in it. Tbey are the signs of concrete facts — one, two, 
three — which are inconceivable by n3, except in concrete 
instances. The simplest material will answer the purpose — 
bread crumbs, pebbles, mud specks ; but we must have, in the 
mind, a series of discrete impressions, derived somehow or 
other ; even thoughts would do ; but we find it easier to work 
upon things of sense. Without some concrete basis, we cannot 
possess in thought any number whatever. This is merely to 
repeat the received nominalistic view of Abstract Ideas. 

There is, however, an important step that can be made in 
Mathematical Reasonings, whereby we can altogether leave out 
of sight the concrete things (which is to refrain from realizing 
the very meanings of the numbers that we are handling). We 
can devise rules of operating upon the symbols, which, when 
duly constructed and checked by the proper precautions, will ; 
give us the same results as actual experiments upon the con- 
crete numbers. Having constructed our decimal notation, I 
we can base upon it a multiplication table, containing equiva- 
lent formations of numbers; and by mere force of memory, 
recalling these symbolical equivalents, we can perform opera- 
tions of multiplying, without thinking of the concrete numbers 
at all. In getting out the product of 94 by 116, we can leave \ 
the world of numbered realities out of view for the time : com- 
ing back to it only when the product has to be practically 
turned to use. 

Now, by this dwelling among symbols, and rules and signs : 
of operation, we are as far away from Matter, or things in the I 
concrete, as we can possibly be. If anything represents pure 
Form, the multiplication table does. The higher operations of 
Algebra keep us for longer periods withdrawn from concrete 
reality; but the principle is the same. The symbolical creations I 
are more numerous, the rules of operation more complicated, 
the operations themselves more protracted ; yet there is no- 
thing new in the principle of working. 

The question then arises, Do these rules of operation upon 
symbols bear out the pretensions of Formal Logic, as to the 
self-evident, necessary, and non-material character of Formal 
Thinking ? Are all such rules, in their origin, completely 
withdrawn from the tests of concrete experience, as they are in 
the working ? The full answer to this question is the theory 
of Deductive Reasoning in general, and of Mathematical Rea- 
soning in particular. It is enough here to make two observa- 
tions. First. If it be true, as the a posteriori thinkers maintain, 
that the final axioms of all Mathematics, — on which repose the 



FORMAL KULES OF OPERATION. 

mles for Arithmetical sums, for Algebraic e for 

Geometrical demonstrations,— are induct ions 

then these various rules of operation 1 

material source, and are not evolved by the mind in 

or formal thinking. 

But secondly. It is notorious and undeniable, I 
of operation, before they are trusted to, arc tried and che 
by the results. A great many of them arc 
unpromising, and even repugnant, to the ordinary n 
they are admitted only because of their being instrument 
bringing out true results (as proved by 
matter). Who would put faith in such a rule as l minus mul- 
tiplied by minus gives plus/ unless fully assured by 
trials that it leads to correct conclusions ? The impof 
quantities of common Algebra, the infinitesimals of the higbee 
Calculus, have been a perpetual stumbling-block, as 
their Form ; their sole justification is the test ol actual ;. 

Seeing how many ingenious tricks can be played upon us 
by formulas and formalities, the most unexceptionable in tin it- 
appearance, there probably is not a single rule in the w 
compass of Mathematics that any reflecting person would trust 
to merely as a 'Law of Thought,' without an appeal M 
matter by actual trials. The reason why we are so confident 
in these rules, is that their verification is so easy, and has I 
so complete. But in the absence of verification, we should 
very chary indeed in admitting such rules as the mnltipl 
tion and division of fractions, vulgar and decimal, the extrac- 
tion of the cube root, and the like. ^Ve havt 
deceived by more plausible formalities than these ; dolus 
in generalibus, is true of all alleged ' Laws of Thought.' 

The same remark as to the necessity of indu 
tion applies to Logical Forms. Not one of the valid m 
would be received by mankind upon formal evidence a; 
The dictum seems very evident, the nota mot<B even i: 
dent; but the nota notce conducts us most plausibly to ; 
conclusions, until by examination of the actual < 
laboriously fenced it with circumlocutions and qualii 

When we examine carefully the various processes 
we find them to be material to the very core. Tak< 
How do we know that, if No X is Y, No Y (a X i I 
ining cases in detail, and finding the equiv 
Obvious as the inference seems on the mere i 
do not content ourselves with the formal aspen. II 
we should be as likely to say, All X is Y I we 



650 THE PROVINCE OF LOGIC 

are prevented from this leap merely by the examination of 
cases. 

Again, tbe laws of Hypothetical Eqnivalence are dependent 
on our knowledge of the material circumstance called Plurality 
of Causes, but for which the formal directions as to Hypo- 
thetical Inference would be quite different. 

Mr. Mansel complains that the rules of Definition commonly 
given in logical treatises are extra-logical ; that is, they step 
out of Form into Matter. The charge is well founded ; the 
writers obviously felt that Definition, confined within the 
narrow limits of the Formal, would be a very meagre affair. 
What would be logical defining in strict form ? Why, 
this. A Formal Definition consists in giving, as the marks of 
the thing defined, the marks of some higher Genus, together 
with the Difference, We have, then, these forms : — The 
Genus together with the Difference (in Connotation) is the 
Species ; the Species minus the Difference is the Genus ; the 
Species minus tbe Genus is the Difference. This is the whole 
theory of Defining, according to Formal L^gic ; and it is worth 
nothing. 

Still more would a logic of Classification, to be of any value, 
trench upon material considerations. Logical Division is 
another name for classification. The rules of Logical Division 
are Formal, but they have to be held in check by the matter, 
otherwise they may lead us astray. 

Ifc may be maintained that Deduction and Induction are 
properly continuous operations ; they are the parts of one 
whole. Within certain small limits, Deductive processes are 
possible, upon rules of symbolical operation solely, these having 
been well fenced by a study of the matter ; but real deduction, 
the extension of a principle to new cases, supposes an exami- 
nation cf the cases in their concreteness or actuality, exactly 
as in the inductive generalization of the rule. The judge who 
applies the law must look to the matter ; he must not commit 
paralogisms of form ; but he cannot stop short at mere formal 
correctness. 

Within the Inductive sphere, we might construct rules of 
Formal operation, such as ought to commend themselves to a 
rigid formalist. Thus, A, B, and C, beifig joint causes of an 
effect X ; if A be reduced in amount, B or C must be corres- 
pondingly raised to keep up the effect ; if A be increased, the 
others are so far dispensed with, and so on. These are easy 
mathematical considerations, which we know to be correct 



VALUE OF A LOGIC OF INDUCTION. 

generally, and can therefore nso formally without n— ml to 
the matter. 
I 

But the question at issue cannot bo adequately itattd 01 
we view Logic as a Practical Science. It its | 
is conceded, the propriety of extending the 1' 
upon the utility of rules for Induction. The preSQO 
favour of such rules are these : — 

First. It is admitted that Aristotle included in bi 
both Deduction aud Induction, however imperil 
been his view of their respective spheres, and howevrr ii 
quale may have been his handling of Induction. Thn 
testimony of the Founder of Deductive Logic is oppti 
exclusive pretensions. 

Secondly. In the table of Fallacies, sketched by Arisl 
and retained by the scholastic logicians, with slight mod 
tions, there are comprised Fallacies of the Matter, and of 
these some are fallacies of Induction (?wn causa pro causa, &t). 
From this we may infer, that, in the opinion of Logician! 
generally, people are liable to commit mistakes in regard to 
matter, no less than in regard to form. We may inter huth.r, 
that it is not useless to give a reminder of these material and 
inductive mistakes, which is, in fact, a Logic of Induction. 

Thirdly. The scholastic period was marked by an ah 
exclusive attention to the formal or Syllogistic part ot % L 
At the revival of letters and philosophy in the loth and iuth 
centuries, public opinion revolted against the narrow ik- 
the conception, and found a spokesman in Bacon, who iimu un- 
rated, amid very general applause, a Logic of Induction. For 
the last two centuries and a half it has been the pfid 
both physical and metaphysical philosophers to call thenm 
his disciples as regards the methods of pursuing loienea 
philosophy. 

Fourthly. The renovated Physics, or Natural Philosopb; 
Galileo and Newton was accompanied with a professed L 
of Induction — the famous lingulcs Pkilosophaiidi pn 
the Third Book of the Principia. These rules, meagre M tbej 
are, were a guiding star in physical research to the aftqc 
of the 18th century. 

Fifthly. In the present day, when physical bai been 

Bo far advanced as to exemplify sound methods of pi 
the most distinguished physical philosophers still feel and 
knowledge the need of a systematic guide to rw r the 

more abstruse and subtle departments. The Introduction to 



652 THE PROVINCE OF LOGIC. 



! 



Natural Philosophy, by Sir John Herschel, and the History 
and Logic of the Inductive Sciences, by the late Dr. Whewell, 
are testimonies to this want. 

Sixthly. Since the publication of the work of Mr. John 
Stuart Mill, in which the Inductive Logic is methodized with 
a completeness previously unknown, applications have been 
extensively made of the Inductive canons to the Experimental 
Sciences. The investigations of Medical science have especi- 
ally profited by Mr. Mill's teaching ; a higher and surer stan- 
dard of evidence has taken the place of the loose methods of 
reasoning formerly prevalent. 

Seventhly. The Science of Politics is an equally striking ex- 
ample. The valuable work of Sir George Cornwall Lewis on 
the ' Methods of Observation and Reasoning in Politics,' makes 
perpetual reference to the Inductive Logic of Bacon, Her- 
schel, Whewell, and Mill, and only once or twice alludes to 
Formal Logic, although the author's education was such as to 
incline him to view that department with the utmost possible 
favour. He complains strongly of the wide-spread abuse of 
the Method of Agreement (the enumeratio simplex of Bacon) 
in Politics, as in other subjects ; and endeavours by precept, 
and by example, to counterwork the vicious tendency. 

Eighthly. Sir William Hamilton occupies a considerable 
portion of his Course on Logic (nine Lectures out of Thirty- 
six), with Modified Logic, in which he considers Truth and 
Error, on the material side ; Observation ; Induction ; the 
Credibility of Testimony ; and various other points related to 
the acquisition and communication of knowledge. The plan 
of his course would have allowed him, without contradicting 
his views of the Province of Logic, to have gone as minutely 
as Mr. Mill does, into Induction, and the operations subsidiary 
to Induction, such as Classification and Naming. 

Dr. Thomson, in his Laws of Thought, follows the example 
of Hamilton, in the enlargement of the Province. In Part IV., 
entitled ' Applied Logic,' he considers (shortly) the Search for 
Causes, the Inductive Methods, Definition, Analogy, Chance, 
Classification, Fallacies generally, and the Division of the 
Sciences. 

C. — ENUMERATION OF THINGS. 

The Classification of Names (p. 61) leads by a natural 
transition to the Classification of Things. Moreover, in order 
to establish the most generalized propositions, we must possess 
correspondingly generalized Notions. 



BASIS OF RELATIVITY. 






The totality of Existing Things may be divided [ n 
ways, under different principles of classi Beat ion 
We may partition the whole universe into 
and Terrestrial Bodies ; into Minerals, Plants, A 
Solid, Liquid, Gas ; into Ponderable and Impoud< 
j the Four Elements of the ancients, which division 
J gives the three states of matter, and the impoudera 
I Light, &c. Lastly, we may make a division into 
Mind. These various modes of sub-dividing tin 
| things are useful for their special ptirpos 
I the Logician is to arrive at a division that will oorresp md to 
\ the distinct methods of enquiry, so as to partition the field 
knowledge according to the best division ot intellectual labour. 
We begin by re-stating, as an essential preliminary, the 
I. principle of Universal Relativity, by which all objects of kn<>w- 
I ledge are two-sided, or go in couples. This statement is 
I necessary to obviate the error, committed by Aristotle and 
others, of placing * Relation ' in an inferior or subordin. 
place in the classification. If Relation is recognized at all, it 
is fundamental and independent ; everything comes under it, 
it comes under nothing. The supreme position given by 
Logicians to the * Law of Contradiction * is a mode of admit- 
ting this primary fact. 

I. The deepest of all Relations is Object and Sir.j 
monly called Mind and Matter, the External World and the 
Internal World. 

W T hen we pass from being engrossed with pleasure or | 
to the consciousness of some extended thing, *s a tree, w ■ 
affected with a marked r hock of difference ; we have nui 
transition the broadest and deepest that the mind qm 
pass through. These typify the two ultimate or iiual mod 
the human consciousness ; they mutually constitute each other, 
on the principle of Difference or Relativity ; they 
therefore, be resolved one into the other, or into any I 
fundamental experience. The contrast mq 
the chief division of all things, on the principle of dividing 
upon the maximum of difference. One portion of kuowi* 
we term the Object world, the Extended World, 
correctly, Matter, and the External World. The other paj 
we call the Subject world, the Unextended Mind, and, 
properly, the Internal World. Indeed, when we talk of these 
two departments as dividing between them the an 
existence, we are using fictitious and unmeaning 1 
the ultimate universe, according to the law of Iwlativity, is • 



C 54 ENUMERATION OF THINGS. 

couple ; the highest real grouping of things is this two-fold 
grouping, called Object and Subject, &c. These are the 
proper summa genera. Existence is a mere name. 

11. Object has been variously represented and analyzed. 
Some have contended that it is an ultimate fact, given in our 
earliest consciousness. Others have resolved it into simpler 
states of the mind. The different views on this subject be- 
long to the Metaphysical and Psychological question called ! 
the * Theory of External Perception.' We here assume that the 
notions expressed by fc Object' and ' Subject/ can be analyzed, 
and we give one mode of the analysis. Object means (1) 
what calls our muscular and bodily energies into play, as opposed 
to passive feelings ; (2) the uniform connexion of definite feel- 
ings with definite energies, as opposed to feelings unconnected 
with energies ; and (o) what affects all minds alike, as opposed I 
to what varies in different minds. 

(1) The greatest antithesis existing among the phenomena 
of our mental constitution is the antithesis between the Active 
ind the Passive ; the muscles (with the out-carrying nerves) : 
being the bodily instrument for the one, the senses (with the 
in-bringing nerves) being the bodily instrument for the other. 
To this fundamental antithesis we are able to link the opposi- 
tion of Object and Subject. Although developed by other 
circumstances, the contrast appears to be rooted in our greatest 
Psychological contrast. 

(2) The circumstance of our feelings being definitely changed 
with definite active exertions on our part is a most notable ac- 
companiment of our objectivity. When we move across a 
room, and feel our optical prospect definitely changing with 
every step, and always going through the same definite changes 
with the same movements, we put this experience in contrast 
with feelings that fluctuate when we are perfectly still, and 
have no relation to our movements ; as the stages of an illness, 
the periodic sensations of hunger and fatigue, and the various 
passions and emotions, 

(3) It is a characteristic of the Object world, that different 
persons are affected in the same way. Those definite changes of 
sense, accompanying definite movements, as in walking down 
a street, or in entering a room, arise in each person alike ; the 
other class of feelings — hunger, fatigue, fear — run a different 
course in different persons. 

These are probably the main features of the fundamental con- 
trast of Subject and Object; other subsidary circumstances have 
been pointed out, but their discussion is not suitable to this place. 



ATTRIBUTES OF BOTH OBJECT AND BUM 

III. The Subject is explained by what has been said of the 
Object; it concerns our passive states; our 
finitely changed with definite energies; and the 
different persons vary in the same circaraetan 

IV. There are attributes common to Object and to Sul> 
and attributes special to each. 

Notwithstanding the fundamental contrast of these two ex- 
periences, we can affirm some attributes of both. Thus, within 
e the sphere of each, we are variously affected ; we reeogniie 
I object distinctions and subject distinctions. So we identify 
I and compare object facts with one another, and subject facts 
| with one another. From the very nature of human kn 
ledge, these possibilities of discerning agreemeut and difference 
must hold in both departments. Hence : — 

First. The contrasting attributes of Likeness and Unlike- 
ness belong equally to Object states and to Subject states. We 
identify and discriminate magnitudes, forms, colours, <fcc, 
which are object facts ; we identify and discriminate pleasures, 
pains, volitions, ideas, which are subject facts. Hence, affir- 
mations of likeness or of unlikeness may apply to every kind 
of knowledge whatsoever. Being in fact ttie fundamental cir- 
cumstances that define and constitute knowledge, such affirma- 
tions are analytical propositions. 

Secondly. Quantity or Degree belongs to both states. This 
is Agreement and Difference in one important fact or feature, 
called more and less; the states of the subject mind are all 
of varying amount or intensity, as well as the states of the 
object consciousness, which we call object properties— size, 
weight, hardness, &c. We may and do predicate quantity, 
therefore, of everything knowable. The laws of Quantity, of 
which Mathematics is the complete developement, pervade all 
modes of existence. It is true that numerical calculations are 
mostly confined to object properties — as space, dimensions, 
weight, and so on; we have no numerical ratios in pleasu: 
and pains. This circumstance, however, which is a gr 
drawback to the science of mind, is not due to the absence of 
degree from mental phenomena, but springs from our inability 
to set up an exact common standard of degree in the states of 
the mind, and to take precise measures according to tl 
dard. We are conscious of inequalities in our p1< 
emotions, and desires, but we have a difficulty in filing the 
degrees in an understood expression, such as may bo conmiuui- 
cated to others, and permanently recorded. 

It is usual to specify the leading modes of Quantity under 



656 ENUMERATION OF THINGS. 

Intensity, Duration, and Extension : the last being a mode 
special to the object: Intensity and Duration apply in both 
regions of phenomena. Intensity is usually marked with re- 
gard to each special property — intensity in colour, heat, pres- 
sure, &c. Duration, which is a degree of continuance, is more 
commonly abstracted from things, and enters into that great 
and all-comprehending generality, called Time, to be noticed 
more fully under next head. 

Thirdly. The great and important contrast named Co- exist- 
ence and Succession is found in both departments of pheno- 
mena. 

Co-existence is not an ultimate experience of the mind. 
We begin with modes of Succession, which are developed into 
Co-existences. 

To the mind, which, with very slight qualification, can 
attend to but one thing at a time, all distinctive states of con- 
sciousness are successive. Succession is the law of our mental 
being. The succession may be rapid or slow, which supposes 
the estimate of duration above noticed. In succession is 
grounded the important fact called Number or Discrete Quan- 
tity, as opposed to the measure of continuance, or Continuous. 
Quantity. We identify groups of successions as twos, or 
threes, lours, and so on. Thus the forms and modes of Quan- 
tity are involved in the modes of succession of our sensations, 
feelings, and thoughts. 

Duration and Succession (with Number) thus belong alike 
to states of the Object and states of the Subject. The element 
of Time, which is duration and succession generalized to the 
utmost, and reduced to a common measure, is a property of 
both worlds ; a circumstance that has been noticed from the 
very beginning of philosophy. 

The predicate of Succession also involves order of priority, 
which can apply to object and to subject states equally. 

Co existence is an artificial product, a peculiar mode of suc- 
cession, which in its highest form is Simultaneity in Space, or 
Extension, a property of the Object sphere exclusively. There 
attaches to Mind an inferior mode of Co-existence, the co- 
existence of two or more awakened sensibilities at one moment 
of time. 

Of Attributes common to both spheres, we have thus Like- 
Unhke, Quantity, Succession, Co-existence ; but as the predi- 
cation of Like- Unlike in the widest sense is, from the nature 
of knowledge, a purely identical proposition, we need state 
only Quantity, Succession, and Co-existence. These are the 



ATTRIBUTES SPECIAL TO THE OIU 

three attributes assumed as distributing kno iff or . 

ent heads of Logical Method. 

V. The attributes special to the I 

(1) Extension.— This property is tho turn lm . 

stance ol the object world, the one fact cumin,,, 

is not uimd, or not subject. When we are in u pure] . 

state, as a pleasure or a pain, we have i 

tension or space. The distinction between 

and the unextended mind, explicitly made in the 

A.D., was the commencement of correct vv | ttU 'j 

matter. 

Psychologically considered, Extension is a d 
or moving energies, assisted by our senses. Motion 
tial to the consciousness of things as extended. 
a real property whether with or without matter ; 
motion, even empty space is an actuality. The total of t he 
Extended World is sub-divided into Extended .Matter and 
Extended Space without matter. 

(2) Resistance, Inertia, Momentum, or Force. — Xhi 
characteristic property of Extended Matter, m its oppod 
to an Extended void. The putting forth of our en 

the peculiar mode called Resistance is perhaps the bud] 
situation that we can be in, as regards the active hide of our 
being; hence, resistance may be considered our fundami 
consciousness of the object world. Resistance is Matter; the 
giving way of resistance, followed by movement, 
no subject state have we the peculiar sensibility caiie_d I 
energy, or resistance ; where that feeling is present, we apply 
the name matter. 

Extension and Inertia are the two generic i 
the long known group of attributes called the prt 
of matter; the radical and identifying peculiarity - 
so-called external and material world. {Still, these are in i 
association with other properties, based on j bility, 

or sense proper, as colour, tactile feeling, <fcd 
qualities); which properties, of themselves, would not be 
object properties, but become so by their dependence upon the 
object class. 

(3) Colour.— -The pure and proper sensibility of tl.< 
susceptibility to mere light, is not propel . 

The conjunction oi the feeling with visual ej 
cular sensibility of the eye), and with locom 
to give objectivity to light and colour. Our not; 
extended or simultaneous in space is based on move;. 



658 ENCMEKATION OF THINGS. 






filled tip and defined by our optical sensibility to varieties of 
lio-hfc. Our feelings of illumination are definitely connected 
with definite movements and in tbat way comply with one of 
the grand conditions of objectivity. 

(4) Touch. — The commonly recognized sense of Touch is a 
compound of muscular energy with pure skin sensibility. 
This last, or touch proper, is scarcely ever separated from the 
fundamental experience of Force or Resistance (we may make 
the separation by supporting the outstretched arm or leg). 
Hence, touch is adopted and embodied among object properties. 
The tactile effects, called hard, soft, rough, smooth, are quali- 
ties of Matter. 

Sight and Touch are the senses most completely incorporated 
with our activity, or with our object experience. The remain- 
ing senses have a looser connexion with our energies, but, so 
far as connected, we rank their indications among object 
qualities. 

(5) Sound. — Mere noise might be a form of simple subjec- ' 
tivity. When related to movements, as when steadily increasing 
or diminishing with our locomotion, it falls into a connexion 
with objectivity. So regularly is this connexion observed, that 
the fact is enrolled among properties of matter. 

(6) Odour. — An exact parallel to Sound. The objectivity 
of odour is established by its definite changes under definite 
movements on our part. 

(7) Taste. — There is here a compound of a peculiar sensibility 
— the proper gustatory feeling — with touch proper ; whence 
it comes readily into the object sphere. 

(8) Heat and Cold. — This property needs no other comment 
than the foregoing remarks on Sound and on Odour. 

The various organic sensibilities of our body — Digestion, 
Respiration, &c. — have a strongly subject character; yet, they 
contract object relationships whenever they are definitely 
changed with definite movements, as when we connect reple- 
tion with taking food, or suffocation with impeded breathing. 
But, in so far as they suggest no activities, or attitudes of 
energy, they are pure subject states,modes of self-consciousness. 

These are the various sensible properties of the species 
* matter' in the genus •extended;' they are the modes of 
primitive sensibility that we call material. There are other 
properties of a more subtle and abstruse kind, arrived at by 
the help of our intellectual processes — such as we call Attrac- 
tions, Repulsions, Molecular structure and arrangements — 
which are necessary to completeness in the enumeration. 






ATTRIBUTES SPECIAL TO Til! (559 

The Sciences of the so-called External world 
with the various attributes now described. One p 

Mathematics is occupied with quantity in Extensi< 
embraces the essential tact of Matter, together with 
incidents; Physics and Chemistry include Light, Sound, I I 
Heat, &c. 

VI. The attributes special to the Srn.ir.rr are hfct M 
marks or essential attributes of Mind— / 
Thought. All these are in full antithesis to the 
facts, as above detailed. 

Of Feelings, the greater part are pleasures and pttfc 
are our most unequivocal types of subjectivity. \\V 1 
confound two such things as comfortable warmth, and lit 
chair; the heterogeneous is at its utmost stretch in such a 
contrast as this. 

Our states of Will, or Volitions, have a purely sul 
origin, namely, our feelings, with outcomings in to 
sphere. The two departments are here, as often happen 
close proximity, but are not therefore confused. Voluntary 
action is always reckoned a special characteristic of mind. 
For, although it is activity, directed often upon material tli 
yet its origin in the pleasurable and painful modes of ft 
bility gives it an indelible stamp of the subject. 

Our Thoughts, Ideas, or Intellectual states, have in them a 
considerable amount of object reference ; still there is a I 
distinction between Sensations and Ideas, in the circums: 
that the one class is, and the other is not, connected wit; 
finite bodily movements. The succession of our sen- 
in uniform accordance with our locomotive and other u 
ments ; the succession of our thoughts is totally diuY 
Hence, although our ideas are the reflexion or repetition of our 
sensations, yet their manner of occurrence assimilates them 
with subject states. 

In the complex fact called Sensation, we have i 
shiftings of the scene, from the object to the subject. A 
sation, as cognisant of extension, resistance, colour, etc., is an 
object fact; as a pleasure or a pain, it is subjec , un- 

mistakeable as the contrast is, wide as is the chasm, we may 
leap it a great many times in a minute ; we Battel 
between the pleasurable consciousness of 
the intellectual measure of it as a thing of lis 1, or 

colour. 

The sciences of the Subject World have thus I with 

our Feelings Volitions, and Thoughts They h:-. 



660 ENUMERATION OF THINGS. 

to draw the delicate boundary line between the two worlds, 
to divide the spheres, where they become entangled. 

If it were now asked what, in the final analysis, is the 
nature of predication, we are able to affirm — Attributes of the 
Object, and Attributes of the Subject, declared as related in 
Quantify, as Co- existing or as Successive* 

VII. Substance is not the antithesis of all Attributes, but 
the antithesis between the fundamental, essential, or defining 
attributes, and such as are variable or inconstant. 

From the relative character of the word Attribute, the fancy 
grew up that there must be a substratum, or something dif- 
ferent from attributes, for all attributes to inhere in. Now as 
anything that can impress the human mind — Extension, 
Resistance, &c, may be, and is, termed an attribute, we seem 
driven entirely out of reality, if we would find a something that 
could not be called an attribute, and might stand as a sub- 
stance. 

But ' substance ! cannot be rendered by non-entity. The 
antithesis that we are in search of is made up without so 
violent a supposition. Substance is not the absence of all 
attributes, but the most fundamental, persisting, inerasible, or 
essential attribute or attributes in each case. The substauce 
of gold is its high density, colour, lustre, &c. — everything that 
we consider necessary to its being gold. Withdraw these, and 
gold itself would no longer exist: substance and everything 
else would disappear. 

The substance of Body or Matter, is the permanent, or 
essential fact of Matter — Inertia or Resistance. This is the 
feature common to everything we call Body— whether Solid, 
Liquid, or Gas ; the most generalized, and therefore the defin- 
ing property of Matter. The remaining attributes of matter 
vary in each separate kind ; they make the kinds or specific 
varieties — air, water, rock, iron, &c. The real distinction is 
thus between the Essence and the Concomitants, the Invariable 
and the Variable, the Genus and the Species. 

The substance of Mind is no other than the aggregate of the 
three constituent powers — Feeling, Will, Thought. These 
present, mind is present ; these removed, mind is gone. If the 
three facts named do not exhaust the mind, there must be 
some fourth fact; which should be produced and established as 
a distinct mode of our subjectivity. The substance would then 
be four-fold. But the supposition of an ' ego ' or ' self,' for the 
powers to inhere in, is a pure fiction, coined from non-entity f 






mill's classification. 

by the illusion of supposing that because attribai i to 

something, there must be something th;t; bed 

as an attribute. 

Mr. Mill, as the result ofhis analysis gives the followii 

an enumeration and classification of all Nameabl 

4 1st. Feelings, or States of Consci. 

4 2nd. The Minds which experience those fc*e*Ii 

'3rd. The Bodies, or external objects, which i retain 

of those feelings, together with the pov 
whereby they excite them ; these last being included 
compliance with common opinion, and because their 
is taken for granted in the common language Prom which I 
cannot prudently deviate, than because the recognition ot 
powers or properties as real existences appears to be wai n to 
by a sound philosophy. 

t '4th, and last. The Successions and Co-existences, the 
Likenesses and Unlikenesses, between feelings or states of 
consciousness. Those relations, when considered as sub- 
sisting between other things, exist in reality only between the 
states of consciousness which those things, if bodies, excite, if 
minds, either excite or experience. 

' This, until a better can be suggested, may serve as a sub- 
stitute for the abortive Classification of Existences, 
the Categories of Aristotle. The practical application of it 
will appear when we commence the inquiry into the Impoj 
Propositions; in other words, when we inquire wl 
which the mind actually believes, when it gives what is called 
its assent to a proposition. 

4 These four classes comprising, if the classification be cor- 
rect, all Nameable Things, these or some of them mu 
course compose the signification of all names; and of ti 
or some of them, is made up whatever we call a fact/ (L 
Book L, Chap. III). 

The Categories of Aristotle. 

Y?e owe the Categories to the opposition made by Aristotlo 
to Plato's Realism of Universals. Plato viewed E 
Being as belonging only to Universals separated from their 
particulars; they only 'being permanent as contra-' 
the Generated and Perishable. Aristotle held, on 
that. Real Being attached only to the Particulars ; thi 
varieties of Being might be predicated of an individual—//.* 
aliquid, That man, This horse, Ac— but that no Being bad 



gg2 ENUMERATION OF THINGS. 

any reality apart from the individual. The varieties of Being 
that might thus be predicated of a particular individual, he 
enumerated in a scheme known as the Categories (/caT^o/n'ai, 
Fredicanienta). They are as follows : — 

1. Qvoia — Substantia — Substance. 

2. Tloaov — Quantum — Quantity. 

3. {\oi6v — Quale— Quality. 

4. ri/>o'v n — Ad aliquid — Relation. 

5. riot) — JJbi — Location. 

6. riorc — Quindo —Period of Time. 

7. KetaOai — Jacere — Attitude, Posture. 

8. "Ex"" — Habere — Equipment, Appurtenance, Property. 

9. Unetu — Facere — Active Occupation. 
10. Wdaxeiv — Pati — Passive Occupation. 

Mr. Mill points out the more obvious defects of the Cate- 
gories considered as an enumeration of Things. 

* The imperfections of this classification are too obvious to 
require, and its merits are not sufficient to reward a minute 
examination. It is a mere catalogue of the distintions 
rudely marked out by the language of familiar life, with 
little or no attempt to penetrate, by philosophical analysis, to 
the rationale even of those common distinctions. Such an 
analysis, however superficially conducted, would have shown 
the enumeration to be both redundant and defective. Some 
objects are omitted, and others repeated several times under 
different heads. It is like a division of animals into men, 
quadrupeds, horses, asses, and ponies.' 

Hamilton endeavours to obviate this last objection, by cast- 
ing it into a scheme of successive grades of subordination. His 
elucidation is as follows: — * Being (to oV, ens) is primarily 
divided into Being by itself, {ens per se), and Being by accident^ 
(ens per accidens). Being by itself corresponds to the first 
Category of Aristotle, equivalent to Substance : Being by 
accident comprehends the other nine, but is, I think, more 
properly divided in the following manner : — Being by accident 
is viewed either as absolute or as relative. As absolute, it 
flows either from the matter, or from the form of things : if 
from the matter, — it is Quantity, Aristotle's second category. 
If from the form, it is Quality, Aristotle's third category. Aa 
relative, it corresponds to Aristotle's fourth category Relation: 
and to Relation all the other six may be reduced. 
The arrangement would stand thus : — 



HAMILTON ON THE CATEGOMEa 603 

L Substance (1) 

( Quantity (2) 
II. Attribute «< Quality (3) 

(Relation (4) 'Place (5) 
Time (li) 
Posture (7) 

1 Appurtenance (3) 
Activity ( C J) 
Passivity (10) 

There is no evidence that Aristotle saw the division in this 
light; if he had done so, he might have adverted to the mis- 
placement of ' Relation/ which, if it iucludes any of the others, 
equally includes them all ; Substance and Attribute, Quan- 
tity, Quality — are all relationships. Still, the arrangement is 
useful as showing how some of the worst defects may be 
remedied, and as an aid to remembering the list. The four 
first are easily remembered; the remaining six (under Relation) 
may be cast into three couples — Place and Time, Activity and 
Passivity, Posture and Possession or Appurtenance. 

The Categories do not seem to have been intended as a 
classification of nameable things, in the sense of " an enumera- 
tion of all kinds of Things which are capable of being made 
predicates, or of having anything predicated of them." They 
seem to have been rather intended as a generalization of pre- 
dicates, an analysis of the final import of predication, including 
Verbal as well as Real predication. Viewed in this light, they 
are not open to the objections offered by Mr. Mill. The pro- 
per question to ask is not — In what Category are we to place 
sensations, or any other feelings or states of mind, but — Under 
what categories can we predicate regarding states of mind ? 
Take, for example, Hope. When we say that it is a state of 
mind, we predicate * substance :' we may also describe how 
great it is ( 4 Quantity';, what is the quality of it, pleasurablo 
or painful (' Quality'), what it has reference to ( 4 Relation'). 
Aristotle seems to have framed the Categories on the plan — 
Here is an individual : what is the final analysis of all that wo 
can predicate about him ? 

The proper comparison of the Categories is to the Predi- 
cates, and to the Import of Propositions, or the Univ 
Predicates. Comparing the Categories with the Pn 
we see that through both runs the distinction between Funda- 
mental and Concomitant, Essential and Accidental. The lour 
predicables, genus, species, differentia, proprium, are predica' 
of 'substance:' accidens, — concomitance (trvfA^prjicot) embrace* 
29 



664 THE UNIVERSAL POSTULATE. 

all the categories except substance. Other categories that 
substance might be propria, or predications deduced from tut 
essence of the subject; but it is probable that Aristotle, it* 
speaking of * fundamental ' and ' concomitant ' in connectioc I 
with the categories, meant to include propria in the category 
of substance. Probably Aristotle's list of propria had been 
smaller than the list that could be made out now. Secondly, 
if we compare the Categories with the Universal Predicates 
(Co-existence, Succession, Quantity), we see that the Categories 
are more superficial and less ultimate than the later analysis. 
The category of 4 substance 9 (if we do not include propria) 
belongs to the department of Verbal predication : the remain- 
ing Categories are Real predicates, corresponding to the final 
analysis of propositions. As such an analysis, they are open 
to the objection of not being ultimate ; for example, the predi- 
cations concerning * space * and ' time ' may regard ' co-exist- 
ence ' or they may regard 'succession.' More than this, they 
are not adapted to any logical purpose ; they cannot be made 
the basis of logical departments. 

While these comparisons show the bearings of the cate- 
gories as regards Logic, it should be kept in mind that their 
original purpose was simply to exhaust the possible predicates 
regarding an individual, and not either to exhibit a classification 
of nameable things, or to analyze the import of propositions 
with a view to the arrangement of logical departments. 

1). — THE UNIYEKSAL POSTULATE. 

The theory of Demonstration supposes that we come at last 
to something that cannot be demonstrated. Demonstration is 
the referring of a fact to a higher generality, already esta- 
blished ; to demonstrate such higher generality would be to 
find some principle still more general ; a few steps must lead 
us to something that is absolutely final, something whose evi- 
dence is not demonstrative, something believed in without 
extraneous support. 

The edifice of demonstration is not complete until we clear 
out these ultimate foundations, and state distinctly the nature 
of the certainty attaching to them. Let us then ask what are 
the facts to be received without proof, as underiyable, unde- 
ducible, undemonstrable ? 

In probing to the deepest foundations of knowledge and 
certainty, there has often been a confusion of two classes of 
primary facts— the Logical and the Psychological. By the 
Logical primardia are meant the indemonstrable assumptions 



TESTIMONY OF C0NSCI0U8WW. 






at the foundation of all demonstrable truth ; by the IV 
logical, are meant the elementary sensibil; 
whence our complex intellectual prod 
growth, aggregation, or association. Wli u the 1 
tions are, will be stated fully in this q te j the 
foundations are the primary sensibilities arrived •* »u *n 
ultimate analysis of the mind—such a 
Colour, Sound, &o. There may be a partial coin 
tvvo classes of ultimate data; but the coincidence is not neces- 
sarily total; and each must stand on its own grout, 
propriety of an Analysis of the mind needs to be esUbli 
by evidence; hence it must appeal to some first prim 
different from itself; so that the priority belongs to th 
foundations of our knowledge. 

The phrase * Universal Postulate,' proposed by Mr. Herbert 
Spencer, to express the ultimate foundations of certain 
adopted from Euclid. While the subject-matter is quite differ- 
ent in the two applications, there is this common feature, th.it 
in both something has to be begged on one side and gra 
on the other ; one person cannot force another person iuto the 
admission. The basis of all reasoning is something mutually 
conceded between the different reasoners. When an opponent 
accepts a certain first principle, and declares that he will 
abide by all its consequences, we may compel him to accept 
whatever we can show to be a consequence ; but we havo not 
the same fulcrum with the first principle itself. 

In reviewing the modes of stating the primary assumption*, 
we may commence with the so-called Laws of Thought — 
Identity, Contradiction, and Excluded Middle. Th 
ever, are too limited for our purpose. As explained in this 
work, they are laws of Consistency and Equivalence; the 
Formal Logicians suppose them to include also Svlli 
Mediate Consistency ; by no one are they held as furnishing a 
criterion of material truth. 

Hamilton has put forward ' the testimony of C iess ' 

as the ultimate and infallible criterion of certainty. 1U 
presses the reference to consciousness in the 
or precautions : — 

' (1) That we admit nothing, not either an original 
consciousness, or the legitimate consequence ot such a da 

* (2) That we embrace all the original data of C "**• 

and all their legitimate consequences ; and— 



666 THE UNIVERSAL POSTULATE. 






' (3) That we exhibit each of these in its individual integrity, 
neither distorted nor mutilated, and in its relative place, 
whether of pre-eminence or subordination.' (Reid's Works, p. 

747). 

Stated in general terms, this criterion seems unimpeachable. 
But when we come to specific enquiries, we are aware of its 
vagueness and uncertainty. Oar present consciousness must 
be admitted to be our present consciousness ; when we feel 
hungry, we have the fullest certainty that we are hungry. 
The question, however, arises — what does consciousness say to 
facts in the past, and to facts in the future. And strange as 
the thing may appear, people may differ as to what things we 
are actually conscious of, as will be seen presently. 

Mr. Spencer expresses the Universal Postulate under the 
form of the Inconceivability of the Opposite. The only reason 
assignable, he says, for our primary beliefs, is the fact of ' in- 
variable existence tested by an abortive effort to cause non- 
existence/ When the opposite of an assertion is ntterly 
unthinkable by us, we can do nothing but receive that assertion ! 
as true. 

The difficulties attending the employment of this test are 
these : 

First. The examples that are most in its favour are cases ' 
where the opposite is a self-contradiction. I cannot think that 
I do not at present exist, because the two suppositions are in- 
compatible ; the attempt is a violation of the law of consistency. 
So, — ' Motion cannot be thought of without an object that 
moves being at the same time thought of is an instance where 
the two statements give the very same fact ; * motion ' and 
4 a thing moving,' are two slightly different phrases for an 
identical conception. The opposite is pure self-contradiction. 

Now, for all such instances, a postulate of self-consistency 
would answer the same end as a postulate of unthinkableness 
of the negation. 

Secondly. In assertions where there is not mutual implica- 
tion but difference in things conjoined, the inconceivableness 
of the disjunction has arisen from unremitted experience, or 
indissoluble association. This is the case with extension and 
colour ; we cannot think of an object as extended without 
thinking it as of some colour ; the visible form, although a 
different fact from colour, has always been embodied in an 
optical impression of colour. Again, ice cannot, without great 
difficulty, be thought of but as cold ; the visible appearance 



INCONCEIVABILITY OF THE OPPOSITE. 

of ice and the sensation of warmth are repugnant because of 
the strong opposing association. 

The same remark applies to the (proper) Axi<»» 
matics. The iteration of them in experience civ 

J indissoluble link of thought in their favour. We are pi 
cally unable to think their opposites. So with the Lu 
i Axiom of Mediate Consistency. 

Now, with regard to this class of beliefs, it is an open q 
tion, whether the stress should be laid upon the 
| inconceivableness of the negations, or upou the circum> 
that has brought about the inconceivableness, namely, 
unbroken iteration of the facts. Whether are we to lay bold 
of the primary condition, or of its consequence or concoim; 
There seems to be a presumption in favour of the primary 
condition, namely, the unbroken experience. 
I Mr. Spencer himself attributes our inability to conceive the 
opposites of axioms and other strong beliefs to the experi 
of the race accumulated and transmitted to us. 4 Ol)j« 
facts are ever impressing themselves upon us ; our experi 
is a register of these objective facts ; and the inconceivable 
of a thing implies that it is wholly at variance with the re- 
gister.' 

Thirdly. There are propositions admitted by us to be uni- 
versally true, but whose opposites we can well conceive. 
Such is the law of gravity. We can easily suppose that law 
to be suspended. The reason in this case is, that although tho 
greater number of unsupported bodies fall to the ground, sumo 
do not ; smoke and dust may be seen ascending. We learn to 
regard these as exceptions, but they prevent us from having 
an overpowering strength of association between the ah 
of solid support and the descent of a body to the ground. 

Fourthly. Some examples given as unquestionable applica- 
tions of the principle of Inconceivableness are denied by a 
whole school of thinkers. Both Sir W. Hamilton and Mr. 
Spencer maintain that we are under the necessity of believing 
the Persistence of Force; that we cannot conceive either 
Matter or Force as absolutely created or absolutely detetroj (1. 
It is under the first kind of inconceivableness (when 
opposite is a self-contradiction) that this ease is brought ; there 
is no attempt to affirm it on unbroken experience. Tho 
self-contradiction, however, is by no means apparent ; Fbl 
one thing, and its commencement or termination is Beemingly 
a different thing. That aspect of Force whereby, in communi- 
cating itself, it loses the numerical equivalent of what ifl 



C68 THE UNIVERSAL POSTULATE. 

communicated, becomes familiar to us after we are educated in 
mechanical facts ; and we are then prepared to receive the 
doctrine of Persistence. But prior to this experience, which, 
to be sure, is requisite to a clear and precise cognition of 
Force, we can form a conception of force beginning we know 
not how, aud ending we know not how. We are not at first 
struck with any self-contradiction in force arising out of no 
prior force ; the contradiction that we discover at last is a 
contradiction of our experience. 

A still more doubtful example is furnished by the question 
of questions — Material Perception, which Mr. Spencer upholds 
in its popularly received form, on the authority of the test of 
inconceivableness of the negative. Mysterious as is the con- 
sciousness of something out of consciousness, we are, he says, 
obliged to think it. ■ The current belief in objects as external 
independent entities, has a higher guarantee than any other 
belief whatever/ Yet this is the belief that would have re- 
mained undisturbed to this hour, but for its glaring self-contra- 
diction, first exposed by Berkeley, and since by others. (See, 
in particular, Ferrier's Review of Berkeley). Any test of 
belief that guarantees this assumption must needs be repudi- 
ated by the numerous believers in its self-contradictory 
character. There is an evident incongruity in laying down, 
as a universal postulate, what begs the very point in dispute, 
in a leading controversy. 

Fifthly. Mr. Spencer's view, that inconceivableness (where 
there is no self-contradiction) represents 'the net result of our 
experience up .to the present time,' supposes a theory of the 
sources of belief which is liable to great objections. He 
considers that our habitual contact with actual things has 
engrained in our minds an intensity of connexion between the 
ideas of those things proportioned to the frequency of their 
recurrence. For example, Space relations are the most iterated 
of any, and, consequently, our minds are moulded to these with 
the highest possible tenacity. Next are Matter and Force 
relations. In this way, as already remarked, our repugnance 
to form even an idea of the opposites is a proof of the persist- 
ence of the corresponding facts. So that, experience and 
inconceivability of the opposite are convertible statements. 

Now, h may be granted that the contact with actual things 
is one of the sources of belief ; but it is not the only nor the 
greatest source. Indeed, so considerable are the other sources 
as to reduce this seemingly preponderating consideration to 
comparative insignificance. The competing elements are. 






SOURCES OF BELIEF. 






briefly the following :— (1) The innate impel 

mg that what is will continue; and (2) The inihinuT ol 

strong emotions and predilections. Both influences w. 

illustrated afterwards as prevailing causes of err 

;Book VI). There should also be taken into arc 

sircumstance that our strength of association 

the comparative recurrence of the fact, unless our p 

3uch as to encounter the facts in proportion to ti, 

frequency. What is most familiar to nature, m be the 

most familiar to us. We may not see tho world 

central or commanding point of view. The best exanip 

this is our excessive familiarity with one typo of causation 

the human will ; in consequence of which, we represent that 
as the proper and natural type ; whereas, it is an exceptional 
and narrow instance of causal agency. 

There still remains the effect of society in propagating and 
iterating certain propositions in language ; by which i 
no less than by confronting the facts in our own pe 
are moulded to belief in certain doctrines. On the wl 
therefore, when the various agencies operating to form our 
convictions are taken together, the one circumstance 
by Mr. Spencer is so overborne as to render our strength of 
belief no just criterion of the facts believed. 

Sixthly. Nothing is gained by putting under one head, and 
subjecting to a common test, two classes of beliefs so distinct, 
as Self- Consistency and Consistency with Facts. Hitherto, in 
philosophy, these two departments, under various names, have 
been kept distinct. The one is known as Formal Truth, 
Necessary Truth, the Laws of Thought; the other is llafc 
Truth, Contingent Truth, Inductive Certainty. Although the 
most strongly iterated of the laws inductively arrived at tend 
to indissoluble associations, and to a difficulty of thinking their 
opposites — in that way approximating to the truths of con 
ency, this is a mere incident belonging unequally to things 
that are alike true. When the inconceivability occurs, a 
reason can be given for it ; and the reason not beiug aKs 
the same, there is no propriety in disguising the deeper dif- 
ferences by the superficial agreement We are not obliged to 
have only one Universal Postulate. Should there occur two 
very different kinds of certainty, neither reposing on the other, 
our proper course is to assign different postulates. 

On these various grounds, we demur to the test of the 
' Inconceivableness of the Opposite* as the basis of all 
tainty, or as the matter that cannot be proved, but must be 



C70 THE UNIVERSAL POSTULATE. 

asked and granted, before demonstration can begin. "We should 
propose, instead of that test, at least two Postulates, accord- 
ing to the distinction last noted ; perhaps more may be re- 
quisite. 

First and foremost, we should place the Postulate of Consis- 
tency, or Self- Consistency — the absence of self-contradiction. 
This is the basis of Immediate Inferences, or Equivalent Forms. 
It must be conceded as a prime condition of all reasoning, 
discussion, and intelligent communication. Enough has been 
said in regard to it. 

Secondly, there must be some assumption or assumptions at 
the foundation of all inferences or conclusions from Experience 
— some grounds of Material or Inductive certainty. There is 
much more difficulty in deciding what the postulate should be 
for the department of real inference, or whether a single 
postulate is enough. We here enter upon a totally new 
sphere. 

In order to guarantee the conclusions of our experience, 
or to support us in such allegations as — i water quenches thirst,' 
* unsupported bodies fall' — there is clearly demanded, in the 
first instance, a trust in present consciousness. We must assume 
that what we feel, we do feel ; that our sensations and feelings 
occur as they are felt. Whether or not we call this an irresisti- 
ble belief, an assertion whose opposite is inconceivable or 
unthinkable, we assume it and proceed upon it, in all that we 
do. The calling the negation unthinkable does not constitute 
any reason for assuming it ; we can give no reason better than 
that we do assume it. 

The importance of stating this primary assumption is not 
apparent, till we proceed beyond it. We are carried a very 
little way into knowledge by the admission taken by itself; 
we must make some steps in advance, and assume things 
seemingly precarious in their character when compared with 
the decisive certainty of immediate consciousness. 

It is requisite, in the second place, that we should believe 
in past consciousness, or memory. Unless we trust our recol- 
lection, our knowledge is limited to what is now present ; and 
we cannot compare two successive experiences, or declare two 
facts to succeed one another. We have, one moment, the 
consciousness of thirst ; the next moment, we have the con- 
sciousness of a certain act called drinking ; the next follow- 
ing moment, we have the farther consciousnees of relief from 
thirst. The succession of the three steps is a fact or experi- 
ence; but we cannot believe it, unless we believe in the 






THE LEA? TO THE FUTURE. 

recent fact, given in memory, as well as tho pre 
consciousness. 

The belief in memory must therefore be postulated. It 
may be asked, however, are we to believe oar 01001017 « 1 
limits, or, if not, what are the limits to our beliol r li 
be auy circumstance qualifying or Refitting t 
circumstance should be produced as something 
mental, and therefore proper to take the plao* of the MSHO»< 
tion that it limits and qualifies. In short, memory 
believed in; yet the postulate of tho belief is n 
independent and isolated, but leans to some extent on an 
and a different postulate. 

Granting, however, that the belief in memory, as well as 
the belief in present consciousness, is a primary assum; 
we next remark that it comes short of our needs. The most 
authentic recollection gives only what has been; something 
that has ceased, and can concern us no longer. A far 1 
perilous leap remains ; the leap to the future. All our iota 
is concentrated on what has yet to be ; tho present and me 
past are of value only as a clue to the events th at sr 
come. Now, it is far easier to satisfy us of what has been, 
than of what is still to be. 

The postulate that we are in quest of must carry us across 
the gulph, from the experienced known, either present or 
remembered, to the unexperienced and unknown — must pari 
form the leap of real inference. * Water has quenched 0111 
thirst in the past ;' by what assumption do we atlirm tiiat the 
same will happen in the future ? Experience does not teach 
us this ; experience is only what has actually been ; and, 
after never so many repetitions of a thing, there still remains 
the peril of venturing upon the untrodden land of luture 
possibility. 

The fact, generally expressed as Nature's Uniformity, is the 
guarantee, the ultimate major premise, of all Inuu turn. 
4 What has been, will be,' justifies the inference that watt-t- 
will assuage thrist in after times. We can give no reason, or 
evidence, for this uniformity ; and, therefore, the coin>e items 
to be to adopt this as the finishing postulate. And, undou htedly, 
there is no other issue possible. We have a choiee of modes of 
expressing the assumption, but whatever be the expression, the 
substance°is what is conveyed by the fact of Uniformity. 

As nature is not uniform in everything, we have to apply 
a test to discriminate the uniformities from the 
There is a uniformity in the manner of animal generation, but 



672 THE TOIVEBSAL POSTULATE 

not an absolute sameness in the individuals born even of th$ 
same pair. Now experience will not establish uniformity, but 
it will establish exceptions to .uniformity ; it will sift the natural 
sequences and enable us to reject all that are not uniform. Ifc 
does not prove that anything will always be in the fnture 
what it has been in the past, bqt it will prove that some things 
have been uniform in the past, and others not uniform. It 
has at least a destructive certainty. 

Let us word the postulate thus : — What has uniformly been 
in the past ivill be in the future. Otherwise, 4 what has never 
been contradicted in any known instance (there being ample 
means and opportunities of search) will always be true/ In 
the course of our experience, we have seen a great many pro- 
mising uniformities break down. Again, we have found in- 
stances that have never failed ; on such cases, we venture, 
and it is a mere venture, to predict the future continuance of 
the same state of things. We go forward in blind faith, until 
we receive a check ; our confidence grows with experience; 
yet experience has only a negative force, it shows us what has 
never been contradicted ; and on that we run the risk of go- 
ing forward in the same course. 

This assumption is an ample justification of the inductive 
operation, as a process of real inference. Without it, w T e can 
do nothing ; with it, we can do anything. Our only error is 
in proposing to give any reason or justification of it, to treat 
it other wise than as begged at the very outset. If there be a 
reason, it is not theoretical, but practical. Without the as- 
sumption, we could not take the smallest steps in practical 
matters ; we could not pursue any object or end in life. Un- 
less the future is to reproduce the past, it is an enigma, a 
labyrinth. Our natural prompting is to assume such identity, 
to believe it first, and prove it afterwards. 

This third Postulate is, properly speaking, the Postulate of 
Experience. Not only does it involve a hazard peculiar to 
itself, making a broad line between it and the postulates of 
present consciousness and of memory, but it seems to remove 
all the doubts and ambiguities connected with these appar- 
ently more facile assumptions. Nothing can be better evidence 
than present reality, provided we do not mistake an actual 
consciousness for an inference, or a recollection. This diffi- 
culty is got over by comparison of instances, and by the appli- 
cation of general principles, which repose ultimately upon the 
Great Postulate. 

So with Memory. We trust implicitly a recent recolleo- 






FALLACIES IN LANGUAGE (J 73 

tion ; bat as the interval of time enlarges, our trust diminishes. 
A limit has thus to be prescribed, through a comparison of 
experiences, followed by an inference from the p;tst to the 
future, which brings us round again to the assumption of tlio 
future from the past. Hence, whichever way we turn, wo 
find tliis to be the one resting place for the solo of our foot. 

E. — ARISTOTELIAN AND SCHOLASTIC FALLACI 

The Aristotelian is the basis of all subsequent classifications. 
It proceeds upon the distinction between fallacies in Language, 
and fallacies in Thought. 

L Fallacies arising iu Language (In Dlctione, ol impa -r^v 
\egiv). 1. Aequivocatio, Homonymia, b^usw^la • ambiguity 
in a single term. This is a very comprehensive class of fal- 
lacy. One of the examples given by Aristotle illustrates an 
ambiguity in the word 4 necessary/ ' Evil is good, for what is 
necessary (rd Seovra) is good, and evil is necessary. ' What is 
necessary as a means to a desired end is good ; but what 
necessarily results from antecedent conditions may be evil. 
Whately gives, in his Logic, an enumeration of words often 
used ambiguously in discussion. This task belongs as much 
at least to the lexicographer as to the logician. Thus : * Ex- 
pect* *is either what is possible, as that the sun will rise to- 
morrow, or what is right, as * England expects every man to 
do his duty. ' * Old ' means either length of duration, or dis- 
tance of time. As age gives experience, and experience often 
teaches wisdom, there is a disposition to regard the ancients 
as wiser than ourselves. To this Bacon replied, ' we are the 
ancients ;' we inherit the wisdom of the old, and can add to it 
more experience. 

A chief cause of ambiguity is that the signification of words 
is constantly shifting. The word l publish ' formerly meant 
4 communicate ' or ' show,' — ' The unwearied sun publishes to 
every land.' This is now the legal meaning of publish : to 
publish a libel is not necessarily to print it, any communica- 
tion of written libellous matter to another is sufficient. The 
law still speaks of ' uttering ' coin. 

1 Some ' is of interest to the logician, in its two chief senses 
* some at least,' and * some at most/ or some = not none, and 
some = not all. 

The remedy for ambiguity is Definition. 

2. Amphiboly, amphibolia, afifapoXi'a. A sentence may have 
two grammatical renderings, but by preference suggest the one 
intended to mislead. This was an occasional trick of the 



674 ARISTOTELIAN AND SCHOLASTIC FALLACIES. 

ancient oracles. * Aio te, JEacida, Romanos vincere posse/ 
reads as well whether the Romans are victors or vanquished. 
*I hope that you the enemy may slay/ 

3. fallacia comjpositionis et divisionis. Whately defines this 
fallacy as the use of a term collectively in one premise, and 
distributive! y in another. If the term is collective in the 
major premise, and distributive in the minor, it is a fallacy of 
division ; if the collective is in the minor, and the distributive 
in the major, it is a fallacy of composition. 

Five is one number, ^ 
Three and two are five, >• Fallacy of Division- 
Three and two are one number. ) 
Three and two are two numbers, \ 

Three and two are five, > Fallacy of Composition. 

Five is two numbers. J 

Aristotle gives a similar division, — crvpOeot?, or the possibility 
of wrong disjunction, and Statpeai? or the possibility of wrong 
conjunction. His example of dialpeais is : — 

Five is two and three ; 

Two and three are even and odd ; 

Five is even and odd. 
This would be a fallacy of composition, according to Whately; 
and Mr. Poste observes that it is not easy to understand exactly 
Aristotle's distinction, and not worth the trouble. 

4. Fallacia Prosodiae or Accenius, TrpoaicBla. ' This is of 
very trifling consequence, and chiefly noticeable because of 
the different meanings that may be given to a sentence by 
varying the emphasis. Mr. De Morgan remarks that the 
commandment, ' Thou shalt not bear false witness against thy 
neighbour/ is often read with the emphasis so placed as " to 
suggest that subornation is not forbidden, or that anything 
false except evidence is permitted, or that it may be given for 
him, or that it is only against neighbours that false witness 
may not be borne.' Most of the old examples are mere puns. 
* Tu es qui es ; quies est requies ; ergo, tu es requies.' 

5. Fallacia figurae dictionis, oyr\vLa \tgews. According to 
Aristotle's view, this fallacy is a species of grammatical 
mistake, arising from the circumstance that unlike things 
have names with a like inflexion. Thus, ailing and cutting 
have the same termination, but one applies to a state or 
quality, the other to an action. 

II. Fallacies in Thought (Extra Dictionem, ol efio tr^ \cgeus). 
1. Fallacia accidentia, or a dicto simjpliciter ad dictum 



FALLACIES IN THOUGHT. C7:> 

teenndum quid, *#pa ro ro/t/fe^i/jco'r. A fallacy assuming that 
Bubject and predicate have aJl their attributes in common. It 
is taking a predicate as co-extensive with a subject, when it 
is not. 

k 2. Fallacia a dicto secundum quid ad dictum simpliciter, 
to cnrXtvs y prj Mw? a\\a -irrj // not) y note y irpos ti X^paOm, 
confusion of an absolute statement with a statement limited in 
manner, place, time, or relation. 

What you bought yesterday, you eat to-day \ 

You bought raw meat yesterday ; 

You eat raw meat to-day. 
This is the converse of the fallacia accidentis ; many of the 
examples of both are instances of erroneous conversion of an 
universal affirmative. 

3. Ignoratio fhtnchi) ro Trapa tj)i/ tuv i\e^\ov u^vomv, an 
inadequate notion of confutation. A debater undertakes to 
contradict and overthrow a thesis, and proceeds to destroy 
some different position. It is the common error of arguing 
beside the point, of proving what has only a superficial 
resemblance to the conclusion, or of simply trying to distract 
attention from the point at issue. Mr. de Morgan classifies, 
along with this, any attempt to transfer the onus probandi to 
the wrong side. 

4. Fallacia consequentis, non sequitur, to napa to liro^e.vov. 
To mistake gall for honey, because it is yellow, is a non 
sequitur. Rain wets the ground, therefore wet ground implies 
that it has rained. Every one in a fever is hot, but every 
one that is hot is not in a fever. In this case also, the ex- 
amples are generally instances of wrong conversion of an 
universal affirmative. 

5. Petitio Principii, to irapa to iv apyij \auf3dvetu Aristotle 
describes five forms of this fallacy. (I) When one begs the 
very thing that ought to be demonstrated. (2) When one 
begs universally, what ought to be demonstrated particularly. 
(3) When one begs the particular to help to prove the uni- 
versal. (4) When one begs all the particulars that compose 
the universal. (5) When one begs something necessarily con- 
nected with the conclusion. 

Logicians discuss the question whether the syllogism itself 
is a petitio principii. 

6. Non causa pro causa, to fiy ahiov a>9 atriov itOLvai, an 

inductive fallacy, for which another name is, post hoc, ergo 
proper hoc, which is the vice of the delusive induction called 
per simplicem enumeratlonem. Whitfield attributed his being 



676 ARISTOTELIAN AND SCHOLASTIC FALLACIES. 






overtaken by a hailstorm on a certain occasion to his having 
not preached at the last town. 

7. Fallacia plurium interrogationum, to ia TrXet'iv Ipwrfyia-TQ 
ei> Troieiv, is the fallacy of putting more questions than one aa 
one. Why did you strike your father ? It is an easy snare 
to ask a reason for a fact that has no existence. The first 
members of the Royal Society were in this predicament, when 
they tried to explain why a dead fish weighed more than a 
living fish. The answer was, it did not. 

Hardly any addition has been made to Aristotle's list of 
Fallacies by modern writers on the Syllogism* Aristotle's 
principle of classification has been pronounced illogical, and 
new arrangements have been proposed; but his enumeration 
has not been materially increased. 

The arrangement followed in most Manuals of Syllogistic 
Logic, is that adopted by Whately. 

Jftejecting as indistinct the division of Fallacies into those 
in the words (in dictione) and those not in the words (extra 
dictionem), Whately divides them into Logical and Non- 
Logical. The Logical include all cases of insufficient premises 
advanced as sufficient; all cases * where the conclusion does 
not follow from the premises.' Such cases only, he contends, 
are logical in the strict sense : logic having to do only with 
the sufficiency of the premises given for the conclusion based 
upon them. As Non-Logical he reckons all cases where the 
premises are sufficient for the conclusion, 4 where the conclu- 
sion does follow from the premises,' but where either the 
premises are unduly assumed, or the conclusion is irrelevant 
to the point in dispute. To settle whether the premises are 
legitimate or whether the conclusion is in point, passes beyond 
the proper sphere of Logic. 

Such are Whately's main divisions. The grouping of the 
Aristotelian fallacies under them is as follows: — I. He sub- 
divides Logical fallacies into the Purely Logical and the Semi- 
logical. The Purely Logical are Undistributed Middle, and 
Idicit Process of the Major and of the Minor : two errors which 
Aristotle did not enumerate in his list of Fallacies (sophismata), 
whether because he considered them too palpable to be fraudu- 
lently used by a sophist, or because he had sufficiently exposed 
them in treating of the syllogism. The Semi- logical embrace 
all instances of ambiguous middle term. The ambiguity may 
be in the term itself, or may depend upon the context. The 
ambiguity being in the term itself, we have Fallacia JEguivo- 



I 

WHATELY'S CLASSIFCAT105. C77 

tatwnis, and Fallacia AmpJiiboliae. Our author takes an 
opportunity of remarking that a term may have two m< 
from accident (as the term * lig-bt ') ; or from some Con 
of resemblance, analogy, cause and effect, <fcc, between the 
different senses. The ambiguity arising from the context, we 
have Fallacia Com position is et Divisionis.snid Fallacia Ace 
and a dicto secundum quid ad dictum simpliciter. In the 
cases the middle term is not ambiguous in itself, but is used 
with different adjuncts in the two promises. 

II. In the Non-logical or Material group, the premises may 
be unduly assumed, and the conclusion may be irrelevant. A 
premise may be altogether false and unsupported. The only 
guarantee against this is a knowledge of the conditions of In- 
duction. The major premise may beg the conclusion (petitio 
principiij ; being either the very same as the conclusion, and 
differing only in form, or not quite the same as the conclusion, 
but unfairly implying it. So much for premises unduly 
assumed. Turning now to the other sub-division of the Non- 
logical fallacies (ignoratio elencJii, or irrelevant conclusion) , we 
find various modes of shirking the question particularized. 
One way is to lay great stress upon the objections, taking no 
notice of what may be said in favour. Another way is to shift 
ground, either to something wholly irrelevant, or from one 
premise to another. A third way is to escape under cover of 
complex and general terms. And a fourth way consists in 
appeals to the passions and sentiments, ignoring altogether the 
rational grounds of the point in question, (See Book YI). 



THE AXIOM OF THE SYLLOGISM. 
(Supplementary Note to the Second Edition.) 

In pp. 18, 156, 226, 237, 247, 269, the Logical Axiom of 
the Syllogism has been placed under the head of Inductive 
truth. This has not been done without misgivings, as the 
following remarks will show. 

The drawing of a broad line between Immediate and 
Mediate or Syllogistic Inference, and the laying duwn of a 
Deductive Axiom founded on experience as the basis of the 
Syllogism, will be seen to be attended with difficulties. 

The first is the anomalous middle position of the Hype- 



678 SUPPLEMENTARY NOTE. 

thetical Syllogism. If we are bound to bring hypothetical 
inference tinder one or other of the two forms, wc feel that 
our decision is not satisfactory ; the case passes somewhat 
beyond Immediate Inference, and yet does not reach to 
Syllogism. 

There is the same unpleasant doubt about the cases dis- 
cussed in p. 109, and p. 157, where a singular proposition 
has to be treated as a Universal, We cannot, without con- 
siderable straining, make these out either Equivalent proposi- 
tions or Syllogisms. 

The second difficulty is still greater. The question has to 
be raised, whether syllogistic inference is or is not Self- 
consistency. Is the conclusion the mere equivalent of the 
premises, so that to deny it, while admitting the premises, 
would be self-contradictory ? 

That the conclusion of the Syllogism flows necessarily from 
the premises, is generally insisted on. To refuse the con- 
clusion would be to contradict the premises. Indeed, the 
self-contradiction would be as unequivocal as in the denial of 
an immediate inference — all A is B, some A is B. In what 
then consists the distinction, as regards the logical foundation, 
or the kind of certainty, between Mediate and Immediate 
inference ? 

In the Syllogism, the bond of necessary equivalence lies 
between one proposition and two others ; in the immediate 
inference, it lies between one proposition and one other. 
This makes the case a degree more complicated, without 
apparently altering the generic character of the inference ; 
it is an inference contained in the premises ; it cannot be 
refused without contradiction in terms. 

This circumstance of necessary, or self-consistent relation- 
ship should appear in the axiom of the Syllogism. It does so 
in the dictum de omni et nullo. That axiom seems to be a 
necessary truth ; we feel that to deny ifc would be not merely 
to deny a fact, but to deny in one form of words what we 
have already affirmed in another ; which expresses what is 
meant by ' contradiction in terms/ and by the denial of a 
1 necessary ' truth. 

The other form of the axiom — Nota noice—' whatever has a 
mark has whatever that mark is a mark of,' must also be 
necessary, if it is an exact equivalent. We cannot suppose 
that the Syllogism under one form of axiom is an implicated 
or necessary inference — an analytic judgment ; and, under 
another form, an inductive or contingent inference — a syn- 



THE AXIOM OF THE SYLLOGISM. C79 

tbetic judgment ; such a supposition could arise only from 
some great confusion of ideas. 

If, under the guise of nota vofo?., the axiom is exactly equiva- 
lent in substance, as it is in appearance, to the mat hem >i 
axiom of mediate equality — equals of the same are equal — 
it would not be an axiom of self-consistency, or an analytic 
judgment. That axiom may be very evident, may be rftyled 
by courtesy self-evident, bub it is a synthetic judgment ; the 
subject and the predicate are not mutually implicated ; its 
denial is not a contradiction in terms. The subject is * equals 
of the same' — things severally compared to a common stan- 
dard or measure; the predicate is — equal by * coincidence,' or 
by being compared immediately — a totally distinct mode of 
comparison. These two modes are said to concur ; the trial 
by the one mode is a test or mark of what would happen in a 
trial by the other mode. We have an opportunity of comparing 
two things with the same third ; we have no opportunity of 
applying the two things to each other ; we are assured by the 
axiom that the coincidence of the two with the common third 
is proof that they would coincide if we could apply them to 
each other. There would not be a contradiction in terms, 
there would only be a contradiction of experienced facts, if we 
denied that mediate coincidence infers immediate coinci- 
dence. 

Mr. Mill, in the new edition of his Logic, p. 208, states that 
he regards Formal Logic as the logic of mere consistency, and 
the dictum de omni as its axiom ; he does not insist on apply- 
ing to it the nota notce, although he regards that form as the 
proper axiom for the logic of the pursuit of truth by way of 
Deduction ; the recognition of which can alone show how it 
is possible that deductive reasoning can be a road to truth. 
So viewed it is, not self-consistency, but an inductive, con- 
tingent, or synthetic proposition, like the mathematical axiom 
of mediate equals. 

The difference between formal deduction and real deduction 
is the difference between syllogism and inductive or experi- 
mental truth. Real deducticn is the following out of an 
induction, and assumes the uniformity of nature. That the 
men living and unborn will die is a necessary inference from 
' all men are mortal/ but not a necessary inference from the 
actual premise, which is confined to the men that have 
actually died. The real deduction contains three steps : — 
certain individuals possess the attributes called humanity, and 
ako the attribute mortality ; these two attributes have been 



G80 SUPPLEMENTARY NOTE. 

conjoined through all our past experience ; hence the presence 
of the one marks the presence of the other. Now, John Brown 
and William Smith possesses the first fact, humanity, therefore 
they possess what it marks, that is the second fact, mortality. 
This is the application of the nota notce in its purity and sim- 
plicity ; the uniformity of nature being supposed in addition. 

For greater clearness, take another instance. * All inert 
substances gravitate ; ' throughout all our experience, the 
property 4 inertness \ is a mark of the property 'gravity/ 
Now, the etherial medium in space has the mark inertia (by 
resisting the comets) ; it therefore gravitates. 

But still the question recurs, might not the inference in 
both these instances be given under the dictum de omni ? 
For, basing on the uniformity of nature, we at once convert 
the special observations into a general law ; men in the past 
have died, men in the future will die; whence all men are 
mortal. Caius has the marks of man, is a man ; Caius is 
mortal. Inert matter gravitates ; the ether is inert ; the 
ether gravitates. 

It would thus seem that the attainment of new truth by 
the way of deduction, does not imperatively demand any 
change of axiom. The dictum and the nota not(B are equally 
suitable. If so, the inference must still be a case of necessary, 
implied, or self-consistent truth. Of the dictum and the nota 
noto3 alike, we must declare that their denial is a self-contra- 
diction. 

Necessary or self-consistent inference, instead of being con- 
fined to the manipulation of the equivalent forms of pro- 
positions, takes a wider sweep and embraces the Syllogism, 
which we should have to characterise as ' mediate self-con- 
sistency,' • mediate necessity/ ' complex implication.' The 
forms lying between immediate inference or propositional 
equivalence, and mediate inference or syllogistic equivalence, 
would be regarded as incidental varieties of Self-consistency ; 
they need not be forced under either of the two principal 
genera. 

When we .say f Socrates was wise/ l Socrates was poor ; * 
therefore * one man was wise and poor/ we draw a necessary 
or self-consistent conclusion, but not by the way of the 
Syllogism, as representing deductive reasoning. From 
1 Socrates is wise/ and c Socrates is poor/ we can conclude 
'Socrates is wise and poor ;' \ wisdom and poverty are con- 
joined in Socrates ; • the axiom or assumption here is — when 
properties can be affirmed of a subject separately, or in separate 



THE AXIOM OF THE SYLLOGISM. g31 

propositions, they may be affirmed conjunctly, or in a 
pound proposition. Again, to proceed to the "farther 
—one man was wise and poor — we perform the process ot 
stituting for 'Socrates' the designation * one man/ which prop- 
erly applies to him. This is the mode of equivalence con- 
stantly assumed in working algebraic equations; where, tor any 
expression, we insert at pleasure another equal to it Nts 
of these modes is the same as the dictum de omni, and, there- 
fore, they need not be forced under the syllogism, although they 
amount to something more than stating an equivalent form of a 
single proposition. 

F.— ANALYSIS AND SYNTHESIS. 

The common idea — Analysis and Synthesis — is difficult to 
express adequately, owing to the variety of its applications. 
Chemical Analysis, Mathematical Analysis, Logical Analysis, 
with the corresponding Syntheses, have a basis of agreement, but 
with points of difference. 

The general idea of Analysis is separation; of Synthesis, 
composition or combination. Yet the contrast does not alto- 
gether correspond to the distinction of Abstract and Concrete. 
Analysis is Abstraction, but Synthesis is not the negative or 
the absence of Abstraction ; it is not the un-abstracted Concrete. 
While the scientific man is, by the law of his beinor, an analyst, 
the poet or artist, who does not analyze but combines, is not a 
synthesis!. Synthesis in contrast with analysis, is combining 
after analyzing. 

The simplest exemplification of the two correlated processes 
is seen in Chemical Analysis. The Chemist operates upon an 
unknown mixture or combination of substances, as a strange pro- 
duct from a furnace, or the stomach of a poisoned man. He 
separates and identifies the various ingredients of the compound. 

The obverse Synthesis would consist in making up the given 
compounds by means of the several elements in their proper 
proportions. Thus, having ascertained the precise constituents 
of a mineral water, it is then possible to form the water artifi- 
cially. If the artificial water is exactly identical with the natural 
water, both the analysis and the synthesis are successful 
oorapiete. It is by the analysis, however, that the synt' 
baa been possible. The analysis is the foundation of a new 
means of production; it enables us not merely to imitate and 
rival the spontaneous products of nature, but also, if need 



682 ANALYSIS AND SYNTHESIS. 

be, to vary those products on a definite plan or purpose. Wo 
may introduce beneficial variations into the syntheses of 
miuerai waters. So, having analyzed some crude substance 
medicinally valuable, we may artificially compound it, first, 
literally (which proves the sufficiency of the analysis), and 
nej.t with improved adaptations tor the end. 

The most notable application of Chemical synthesis is to 
the formation of organic compounds in the laboratory. By a 
foregone analysis, the chemist has discovered the constituent 
elements of these compounds, and the peculiarities of their 
union ; he then uses his knowledge to re-produce by laboratory 
processes what has been produced in the course of living 
growth. In this way, urea, acetic acid, and many other or- 
ganic products have been obtained by laboratory synthesis. 
Such synthetic efforts are the trophies of analysis. 

Our next example may be termed Logical Analysis ; it is 
the ordinary Scientific Analysis, the peculiar case of Mathe- 
matics being reserved. Here, Analysis is substantially iden- 
tical with generalization, whether of the notion or of the pro- 
position. What Synthesis is will appear presently. 

The processes of assimilating, identifying, classing, general- 
izing, abstracting, defining, are the various sides, aspects or 
stages, of one fundamental operation. Now Analysis is merely 
a farther aspect, another side, of the same proteus. To identify, 
classify, and abstract, is to separate or analyse, so far as the 
case admits ; the separation being no longer actual, as in 
Chemistry, but mental or ideal. To identify and classify 
transparent bodies, is to make abstractive separation, or ana- 
lysis, of the property called transparency ; or to view its func- 
tions, powers, or agencies alone and apart from all the other 
powers possessed by the individual transparent bodies. Water 
is liquid, but this aspect is disregarded ; diamond has extra- 
ordinary refractive power but no notice is taken of it ; the 
two substances are studied merely in their agreement in what 
we call transparency. 

Now the investigation of nature turns exclusively on this 
abstractive separation. Bodies are constituted with a cluster 
of powers or properties inseparably combinated, yet each 
pursuing its independent course* without any disturbance from 
the others. Water, as transparent, has a power exactly iden- 
tical with diamond and rock crystal, as transparent; the other 
peculiarities wherein the two bodies stand widely contrasted 
have no relevance, exercise no interference, as regards the 
transparency. Hence, the mind, having very limited powers 



ANALYSIS MEANS ABSTRACTION AND INDUCTION. 

of attention, and being easily impeded and thwarted by dis- 
tracting circumstances, finds the ad van 
allied properties, and concentrating its p 
6ubject of study at the time. 

Thus, Abstraction and Analysis, if not ideal the 

same fact viewed with a slight difference. Ahs? 
separately viewing one point of agreement, and leavn, 
other accompaniments in the shade; the transj.. 
Studied by itself, the specific gravity and all other 
rated properties being left out of sight. Anal) 
very same thing ; only, proceeding a little farther, it 
that every one of the powers of a given totfereto, as + 
may be abstracted by turns, — transparency, liquidity, s|» 
gravity; so that water as a whole may be analyzed", or * 
rated (mentally) into a number of different powers, whose 
enumeration is a full account of the agency of water. 

The farther we push abstraction and generalization, the 
farther we push Analysis. When, after generalizing all 
mechanical movements, and forming an abstract idea, or 
analytic separation of molar or mechanical force, we pr< 
to identify mechanical momentum with molecular forces, wo 
make a new analysis ; we separate the property of force from 
its exclusive connexion with the movements of masses, and 
view it as the movement of matter, whether in larger or in 
smaller aggregates. 

It is now requisite to assign a correlative meaning of Syn- 
thesis. As Analysis is the ideal separation and separate exhi- 
bition of all the functions of a concrete thing, as water, iron, 
blood, Synthesis is the re-statement of the whole in their 
aggregate. Its efficacy would be shown in supposing a new 
aggregate, as a liquid diamond, a metal with all the propel 
of lead except its corrosion. It would also be exemplified in 
the act of communicating, by description, the knowledge of a 
mineral, apart from a concrete specimen. 

Another step is inevitable. As these abstractive properties, 
or notions, are what enter into the inductive gem ns of 

nature, each inductive law being two or more coupled 
Analysis becomes applied to Inductive discovery. There can 
be no wide induction without a correspondingly wid< 
lization of at least two notions, that is, without .dent 

analytic separation. The summit of generalization, in 
notions Quantity, Inertia, Gravity, Persistence, is the summit 
of Analysis. The highest generalities of Mind are attaiued 
through the most thorough Analysis of Mind. 



681 ANALYSIS AND SYNTHESIS. 

The employment of Analysis to signify Induction appears in 
Aristotle, and pervades the logicians after him. (See Hansel's 
Aldrich, App. G, Hamilton's Logic, II., 2). By an easy 
transition, Synthesis would be applied to Deduction. The 
deductive operation of following out the law of gravity to 
. lunar perturbations, to the tides, to precession, &c, would be 
called synthetical, as reuniting abstract elements into new 
combinations. Having mastered the laws of central force, 
and the composition of forces, Newton deduced or inferred the 
orbits of bodies governed by other forces than gravity. 

Synthesis, however, scarcely applies to simple Deduction, 
the following out an induction to a new case, as when we infer 
the death of the reigning pope from the mortality of the men 
that have died. There is no element of combination in such 
cases, there is but the filling up of the Induction, which is 
only formally complete so long as any particulars are still 
outstanding. The synthetic operation is best realized by the 
complex deductions, or the union of several deductive laws to 
a composite or concrete case — a secondary law. 

There is nothing gained by using the terras Analysis and 
Synthesis to the Inductive and Deductive processes respec- 
tively. We may show in what way the application is proper 
or admissible, and that is all. 

The use of the Syllogism may be expressed as analyzing or 
separating, out of regard to our mental infirmity, the three 
parts of a step of reasoning, so that they may be studied in 
separation. The premises, instead of being confused together, 
can be looked at apart, and each judged on its merits in its 
isolated condition. This is an advantage belonging to Method, 
or Discovery. Wherever a separation of this kind can take 
place, a great relief is given to the understanding, with a 
corresponding enlargement of its powers. 

An accountant separates his columns of debit and of credit, 
and classifies under different heads payments that relate to 
different subjects and follow different rules. 

Grammatical Analysis may be followed by Grammatical 
Synthesis, as in constructing sentences upon new types sug- 
gested by putting together the component elements in various 
ways. 

Criticism is a species of analysis; and the composition of 
an Oration or a Poem, by the guidance of critical and rheto- 
rical rules, is a strictly synthetic operation ; the previous 
analysis is the foundation of the method. Composition, with- 
out any rules, is not synthesis 



MATHEMATICAL ANALYSIS. 






It is a weakness of the unscientific man to supposo thnt a 
concrete thing, as, for example, a political institution, <-.,„ bt 
viewed only as a whole— that its operations are an indmahlfa 
totality. Thus, the obtaining of justice by t\w prdewllirc in ft 
court of law is through a series of steps and processes— rai iog 
the action, appearing by counsel, summoning a jurv, an, I k> 
on. The effect of the whole being good, the un-aualvzin- mind 
distributes the merit equally over all the parts, andifl 
when a doubt is raised as to the utility of any one constituent, 
as, for example, the jury. 

To advert finally, to the special instance of Mathem 
Analysis and Synthesis. A new step in geometry ma 
taken either by analysis or by synthesis. The various ( 
metrical properties are said to hawe been first discovered, by 
analysis, while in exposition they are in the form of syntlx 
which is not strictly the fact ; we may proceed from the known 
to the unknown in both ways ; discovering new properties by 
synthesis no less than by analysis. 

Let us take Synthesis first, as suiting the case of a science 
whose onward march is by the way of Deduction. Let us 
assume that a certain proposition has been arrived at,* no 
matter how, say, 'Parallelograms on the same base, and be- 
tween the same parallels, are equal.' Now any one consider- 
ing this proposition might readily see, that the axiom of 
mediate equality applied to it, would show that the same 
thing might be predicated of equal bases ; such an inference 
would be an effort of pure deduction, or the skilful combin- 
ing of two already established propositions to yield a new 
third proposition. So, by a repetition of the same apposite 
union of truths possessed, one might also infer that i Tri- 
angles on the same base, or on equal bases, and between the 
same parallels, are equal.' By farther combinations, the rea- 
soner might go on to deduce or infer the 47th, and so forth. 
All which is a purely synthetic operation ; and geometrical 
truths may be evolved to any extent in this way. Corollaries 
are usually deductive inferences, of short leap, from the main 
proposition. The operation is seldom one of simple deduc- 
tion, there is usually a certain concurrence of two or more 
propositions to the new result; and the mental effort li< 
brincinc these together. Geometrical synthesis and deduc- 
fcion are thus the same thing. 

What then is Geometrical Analysis ? Is it Induction ? We 
are told that it proceeds from the unknown to the known. If 
one were to suspect or surmise (without being sure) that the 



686 ANALYSIS AND SYNTHESIS. 

square of the hypothenuse of a triangle is equal to the 6um of 
the squares of the sides, and assuming it, were to endeavour 
to connect it by a thread of geometrical /reasoning with the 
established propositions of geometry, the operatioa would be 
called analytic or regressive, as compared with the synthetic 
or progressive course above described. Yet in reality, the 
mental operation is substantially the same in both; the two 
differ only in superficial appearance, like the enquiry from 
cause to effect, aud from effect to cause. Assuming the truth 
of the surmise first, we have to consider what prior proposi- 
tions would be requisite to support it ; and, again, what other 
propositions would support these ; until we come at last 
upon admitted theorems. The real operation at each step is 
a deductive one ; we feign a proposition and try its conse- 
quences ; if these coincide with the case, such proposition or 
propositions are what we need ; and if they are found among 
the true propositions of geometry, we have made good oar 
point ; we have proved our surmise, and put it in the trkin of 
geometrical deductions. 

The facilities for this inverted deduction are so greatly mul- 
tiplied by Algebra as to give to the algebraic processes the 
designation * analytical ' by pre-eminence. In an Algebraic 
equation, we work backward from the known to the unknown ; 
yet it is by a series of properly deductive operations — the 
application of axioms and theorems already established. 
Algebraic Geometry is called 4 Analytical ; ' the more recon- 
dite processes of Algebra are called the Higher Analysis. 

Thus, while Synthesis has throughout a reference to the 
deductive and combining processes of science, Analysis relates 
to generalization or induction, everywhere except iu Mathe- 
matics, in which it is merely the mode of deductive synthesis 
adapted to the solution of special problems. The geometer, 
when he has no special end in view, evolves new propositions 
by direct or progressive synthesis ; when he has a problem to 
work out, he confines his deductions to those that lie in the 
approaches to the desired solution. The course of discovery 
in a Deductive science can be only Deductive ; it Consists in 
following out generalities in hand to new applications ; usually 
by combining several in one application. The art, the labour, 
lies in the union of several propositions to a result. The 
operation must be tentative ; it cannot be foretold ; yet it is 
amenable to a certain general method, which practice instils, 
and which is not altogether beyond the reach of precept. 



BACON ON THE NECESSITY OF FACT9. 0^7 



G. — GROWTH OF THE LOGIC OF INDUCTION. 

Previous to Mr. Mill, the principal contributors to the Logic 
of Induction were Bacon, Newton, Herschel, and Whewell. 

Bacon. — The essential part of the service rendered by Bacon 
to Science was his protest in favour of basing generalities on a 
patient collection aud accurate comparison of facts. It was 
too much the custom, he complained, to 'just glance at experi- 
ments and particulars in passing ;' in place of this, he proposed 
to 'dwell duly and orderly among them.' With the whole 
force of his eloquence he discouraged nighty speculation and 
rash conjecture, and urged that generalities must be founded 
upon a wide comparison of particulars. 

Following up his emphatic enunciation that men must have 
done with rash speculations and rashly abstracted notions, if 
they desire to make progress in their knowledge of Nature, he 
devised modes of elucidating truth by the comparison of 
instances on a methodical plan. He directs the arrangement 
of facts in three different tables. The first table is to contain 
instances agreeing in the presence of the phenomenon to be 
investigated ; this he calls a Table of Essence and Presence 
(Tabula Essentiae et Praesentiae). The second table is to con- 
tain instances wanting in the phenomenon, but otherwise 
allied to the instances where the phenomenon occurs, each 
instance corresponding as far as possible to some one instance 
in the first table ; this he calls the Table of Deviation, or of 
Absence in Allied Instances (Tabula Declinationis, sive Absen- 
tiae in Proximo). The third table contains the phenomenon in 
different degrees, and is called the Table of Degrees or Table 
of Comparison (Tabula Graduum, sive Tabula Comjpantiva). 
The constitution of the three Tables is exemplified upon an 
enquiry into the phenomenon of Heat; for the prosecution of 
which are assembled no less than 27 instances agreeing in the 
presence of heat, 32 allied instances agreeing in its absence, 
and 41 instances of heat manifested in different degrees. 

The three Tables seem designed for the convenient applica- 
tion of the three leading methods of Inductive elimination — 
Agreement, Difference, and Concomitant Variations; but we 
must not suppose that Bacon realized anything like the 
precision of those methods. He did not conceive the idea of 
choosing his instances so that they should differ in every point 
but the phenomenon under investigation, agreeing only in that 
— the fundamental idea of the method of Agreement. Nor did 
he conceive the idea of the decisive method of Difference, the 
30 



688 GROWTH OF THE LOGIC OF INDUCTION. 

choice of two instances agreeing in every point save the given 
phenomenon. Having collected his Tables of Instances, he 
went to work by excluding according to certain canons the 
irrelevant instances, then making a hypothesis or guess at the 
truth, and finally verifying this by farther enquiry. 

Bacon takes especial credit for his process of Exclusion or 
Rejection. He contrasts it with the popular method of pro- 
ceeding by Simple Enumeration, that is, by counting only the 
favourable instances, overlooking the unfavourable ; and he 
claims to be the first to make it prominent. The problem of 
Induction being to 4 find such a quality as is always present or 
absent with the given quality, and always increases or 
decreases with it,' ' the first work of true induction is the 
rejection or exclusion of the several qualities which are not 
found in some instance where the given quality is present, or 
are found in some instance where the given quality is absent, 
or are found to increase in some instance where the given 
quality decreases, or to decrease when the given quality 
increases.' 

It will be observed that this process of exclusion, although 
a great advance upon generalizing without regard to contra- 
dictory instances, is very rudimentary. Bacon does not dis- 
tinguish between laws of simple Co-existence and laws of 
Causation. The first of his principles of Rejection is suited 
only to the establishment of co existences, and amounts to this, 
that we are not to declare two qualities universally concomi- 
tant, if in certain instances we find one absent when the other 
is present. His other principle of rejection is the reverse of 
the method of Concomitant variations, a disproving of causal 
connexion on account of independent variation ; and applies 
to causation alone. 

As to the modes of certifying the hypothesis allowed after 
this process of collecting and sifting instances — the Logic of 
Proof, Bacon has left us but a fragment. Of his nine divi-- 
sions of aids to Induction, he completed only the first, Prero- 
gative Instances. Under this head, he dictates a farther 
enquiry into particulars,* and dwells upon instances of special 
value to the inquirer, calling them Prerogative from that cir- 
cumstance. To call this division of his subject an aid tc 
induction is misleading ; we expect to find an account of 
instances particularly suitable for founding inductions upon, 
and find instead illustrations of various maxims applicable to 
Definition, Observation, and even Experiment, as well as some 
specially adapted for Inductive Elimination. 






bacon's inductive methods. 

It is among the Prerogative Instances, if any m] a w * 

are to look whether Bacon had conceive I any pi 
for bringing the process of Exclusion or Elimifl 
sitive result, as is done in the modern me til 
and Difference. Under the heading of HuliUry [nstu 
do find a crude approach to the selection of inn! 
in these methods. Solitary Instances are 
that exhibit a phenomenon without any of its 
paniments, as colour produced by the passage of light tin 
a prism; or instances agreeing in everything except 
particular phenomenon, as different colours in the same | 
of marble. He says in a vague way that such 
shorten very much the process of Exclusion. They contain 
really all that is demanded for the methods of Agreement 
Difference. Yet in Bacon's bauds they are comparatively 
useless, and, as part of his method, could not even furnish a 
suggestion f° r more perfect contrivances. The reasons are to 
be found in his vague conception of the problem of ludur- 
His methods of Exclusion are of avail only for problmns of 
Cause and Effect ; they are superfluous for problems of simple 
concomitance, a single instance of disunion being sufficient to 
disprove such a connexion ; yet he speaks throughout as if 
his elaborate comparison of instances were desigued only to 
prove two properties co-existent. To this confusion he w is 
inevitably led by the subjects he proposed to investigate. Ho 
seems to have thought principally of investigating abstract 
qualities of bodies, such as density, weight, colour, volatility, 
porosity, heat ; his purpose being to establish their Form, by 
which he seems to have vaguely understood something inva- 
riably present with these qualities and endowing thorn with 
their peculiar nature. Such an investigation gave amplo 
scope for numerous assemblages of instances ; but the metho is 
of sound knowledge were not likely to be perfected in a region 
that can be approached only by hypothesis. 

Under Migratory Instances, keeping still in view the same 
class of subjects, he recommends attention to cases where 
qualities are produced in bodies ; giving, as examples the pro- 
duction of whiteness by pounding glass and by agitating w 
into froth. From this we gather that ho was sensiolo in a 
measure of the advantage of studying the introduction of a 
cause into known circumstances, although iu his narrow field 
of investigation it could lead to no result. 

In these two first instances we see how far ho antieip 
the Methods of Agreement and of Difference. Few of the other 



690 GROWTH OF THE LOGIC OF INDUCTION. 

twenty-five instances bear strictly on the Inductive Process, 
With Migratory Instances, he compares Instances of Companion- 
ship or Enmity, such as the universal concurrence of heat with 
flame, and the universal absence of consistency in air ; just as 
when a change is produced, we must seek the cause in some 
added influence, so when a quality is always present in a sub- 
stance, we must seek the cause in some property of that sub- 
stance. In Striking or Shining Instances, and Clandestine 
Instances, he urges the importance of the two extremes in a 
variable phenomenon. His seventh and eighth Instances, 
Singular Instances (as the magnet among stones, quicksilver 
among metals), and Deviating Instances (individual monstro- 
sities), are important for alike reason ; their novelty sharpens 
investigation. His twelfth case, Instances of Ultimity or Limit, 
is of the same nature. The five last go together ; the stimu- 
lating efficacy ascribed to them is a favourite topic with 
Bacon, and is the real characteristic of several other Instances. 
Instances of Alliance or Union and Instances of Divorce, the 
thirteenth and fourteenth, form a natural couple. The one 
constitute instances reconciling apparent contradictions ; the 
heat of the Sun cherishes, the heat of Fire destroys ; a con- 
ciliatory instance is found in the growth of grapes in a house 
heated by fire. The second constitute instances disproving 
an alleged universal connection; it is asserted that Heat, 
Brightness, Rarity, Mobility are always found together ; we 
point to air, which is rare and mobile but neither hot nor bright. 

In exemplifying Instances Conformable or of Analogy, he 
breaks clean away from Inductive caution ; he gives as ana- 
logous cases the gums of trees and most rock gems, and refers 
the splendour and clearness of both products to the same 
cause, fine and delicate filtering. Such fancies show how little 
Bacon was removed from the rash speculation he condemned 
in the works of his predecessors. 

His fourteenth case, the famous Instantia Crucis (Fingerpost 
Instance), is mentioned in the Chapter on Hypotheses, § 7, 
(p. l&r), and is there placed in its true light as an instance 
decisive of rival hypotheses. Such instances are otherwise 
called Decisive and Judicial or Oracular and Commanding. 

These are all the instances that have a direct bearing' on 
Induction. Of the remainder, two are of importance for Defi- 
nition, the fifth and the ninth, Constitutive Instances, and 
Bordering Instances. Constitutive instances give the constitu- 
ents of a complex notion ; Bordering instances make the 
baffling transition border between two classes. 



PREROGATIVE INSTANCES OF BACON. 

Five instances are classed together as Tntiamm of the fnwij, 
or of First Information; and relate to Observation, I 
Instances of the Door or Gate he comment! on artificial ai 

the Senses— the Microscope, the Telescope, and r, 
rods. By Summoning or Evoking Instances, lie means m 
tions of things not directly accessible to observation ; 
are the pulse and the urine, as symptoms of the comliti< 
the human body. Instances of the Road, otherwise called 
Travelling and Articulate Instances, display stages of growth 
and of other gradual changes ; — the study of these is strongty 
recommended. Supplementary Instances or Instances of /»' 
are said to supply us with information when the senses entirely 
fail us ; when we cannot remove an agent altogether we may 
vary its influence, and when a phenomenon denes obs er v a tion 
we may study analogous phenomena. Dissecting or A teal, 
Instances are such as great effects produced by small can 
they appeal to our wonder, and stimulate enquiry. 

The seven concluding instances embody advice on the prac- 
tical conduct of investigations. The four first of the seven 
instruct us how to attain precision by definite determii, 
and measurement (Mathematical or Measuring Instances) ; the 
three last how to economize our resouces {Propitious or 1 
voleut Instances). The Mathematical Instances are Tnti 
of the Bod or Rule, otherwise called of Range or of Limit 
(where measurement of Space is required) ; Instances of the 
Cmirse (measurement of Time) ; Instances of Quantity, or 1 
of Nature (where attention is called to the quantity of ad 
agent) ; and Instances of Strife or Predominance, under which 
title he gives a confused enumeration of various * Motions,' or 
tendencies to motion, and represents the movements of h 
as determined by the victory of one or other of these conflict- 
ing tendencies — for example, when water runs out of 
the motion of Continuity is overcome by the motion of Or 
Congregation (the tendency of bodies to the ground). Nothing 
could be more fanciful and illogical than this enumerati- 
4 Motions.' The Propitious Instances are— Intimating In- 
stances, which point out what is most useful to mankind] 
Polychrest Instances or Instances of General Us?, (eontriv 
useful for a variety of purposes, as various modes of exelndiog 
air from bodies to prevent decomposition); finally. Iiutancm 
of Magic, the use of small causes to produce great ell 

We have given no account of the tenth division, Instances 
of Power, otherwise Instances of the Wit or Hand* <>/ Ma» 
is partly identical with awakening Instances : we have singled 



692 GROWTH OF THE LOGIC OF INDUCTION. 

it out here as containing a homily against being led away by 
admiration of skilful contrivances from better ways of accom* 
plisbing the same end* 

In concluding this brief account of the Baconian method 
we may reiterate that the merit of Bacon lay neither in the 
machinery he provided nor in the example he set, but in the 
grand impulse he gave to the study of facts. 

Newton. Newton cannot be said, any more than Bacon, 
to have made a direct contribution to the methods either of 
Discovery or of Proof; but he set an example of rigorously 
cautious enquiry that did more than all the precepts of Bacon 
to raise the standard of Proof, and to purify science of fanciful 
hypotheses. He even went to an extreme and was over- 
rigorous in his requirements of proof; such was his dislike to 
making hypotheses (in the sense of assuming causes not 
known to exist), that he wished to banish them from science 
altogether. 

The Rules of Philosophizing (Eegidce Philosophandi) pre- 
fixed to his Principia were long quoted us authoritative. 
Although worded with an express view to the establishment 
of Gravitation, they are necessarily applicable to other induc- 
tive generalizations. 

The Frst rule is twofold, and may be thus explicated. 
(1) " Only real causes" (verce cansce, actually existing causes) 
" are to be admitted in explanation of phenomena/' We have 
stated the limits to this under Hypotheses (p. 131). (2) "No 
more causes are to be admitted than such as suffice to explain 
the phenomena." This is an echo of the maxim known as 
■ Occam's razor • (* Entia non sunt multiplicanda praeter neces- 
sitatem '), and means that when one cause is proved to be 
present in sufficient amount for the effect, we are not at 
liberty to suppose the presence of other causes. From a few 
words of explanation affixed to the rule, we should gather that 
he meant also to suggest that there was a presumption in 
favour of an explanation accounting for the phenomena by fche 
fewest agencies — a special pleading for his theory of gravita- 
tion : * Nature does nothing in vain, and a thing is done in 
vain by several agents when it can be done by a smaller 
number.' 

The Second rule is — u In as far as possible, the same causes 
are to be assigned for the same kind of natural effects." For 
example, respiration in man and in beasts; the fall of stones 
in Europe and in America. An aspect of the Uniformity of 
Nature designed to favour his view of Solar attraction as the 



NEWTON'S RULES OF PHILOSOPHY 

same kind of effect with the attraction of the r the 

Moon or for terrestrial bodies. 

The Third— "Qualities of bodies that can nc it h, 
nor diminished in intensity, and that obtain in all 1. 
accessible to experiment, must be considered qmftlil 
bodies whatsoever." Another aspect of the Unifi 
Nature, also specially adapted to his extension 
the heavenly bodies. 

The Fourth— * In philosophical experiment, pro] 
collected from phenomena by induction, are to be held, 
j withstanding contrary hypotheses, as either exaetly or ap- 
\ proximately true, until other phenomena occur wherebv 
are either rendered more exact or are proved liable t 
tions.' This is indirectly aimed at the Cartesian explanat i< 
the celestial movements by Vortices, the word hfpothe 
nsed in an opprobrious sense, as involving an element of I 
operating npon imperfectly known materials. The rule may 
be held to imply that the test of a theory is its accordance 
with facts, which is not altogether correct. 

Herschel. Sir John Herschel devotes a considerable por- 
tion of his Discourse on the Study of Natural PhiloHpkif to an 
account of * the principles on which Physical Science relies 
for its successful prosecution, and the rules by which a S) 
matic examination of Nature should be conducted, with illus- 
trations of their influence as exemplified in the history of its 
progress.' His introductory chapters on this head reiterate 
with greater clearness the admonitions of Bacon ; enforcing 
recourse to experience as the sole fountain of knowledge, 
illustrating the dangers of prejudice, and urging the im] 
ance of recording observations with numerical p 
Farther, he dwells upon the value of Classification and 
Nomenclature; although he suggests no leading principle- 
either process. In these preliminary remarks we recognize 
the sagacity of the practised experimenter ; but it is when he 
comes to analyze what is involved in the notion of Cause, and 
to state his rules of philosophizing, that we become fully aware 
of the advance made in the investigation of Nature ■ 
Bacon and Newton, and of the advantage possessed by the 
expounder of scientific method in having & la y of 

successful observations and experiments to generalize irom. 

From the characters implied in the connexion bet v. 
cause and effect, he derives nine ' propositions readily appli- 
cable to particular cases, or rules of philosophizing.' 
them, the second, seventh, eighth, and ninth, are the lour 



694 GROWTH OF THE LOGIC OF INDUCTION. 

Experimental Methods ; which are stated with sufficient pre- 
cision, although not exalted into the prominence given them by 
Mr. Mill as the sufficing and only methods of Proof. By 
Herschel in fact, the four rules are regarded solely as aids to 
Discovery ; the idea of Proof does not seem to have crossed 
his mind. His other rules are more purely suited for Dis- 
covery. The first is a more precise statement of Bacon's main 
principle of Exclusion, the foundation of the methods of Agree- 
ment and of Difference : — 'that if in our group of facts there 
be one in which any assigned peculiarity or attendant circum- 
stance is wanting or opposite, such peculiarity cannot be the 
cause we seek/ The third is ' we are not to deny the exist- 
ence of a cause in favour of which we have a unanimous 
agreement of strong analogies, though it may not be apparent 
how such a cause can produce the effect, or even though it 
may be difficult to conceive its existence under the circum- 
stances of the case ': — a maxim identical with the principle of 
analogy, that we may sometimes infer the presence of one 
phenomenon from the presence of another, although no causal 
connection has been established between them. As an example 
he states that though we do not know how heat can produce 
light, we yet conclude that the sun is intensely hot because it 
is vividly luminous. The fourth rule is that \ contrary or 
opposing facts are equally instructive for the discovery of 
causes with favourable ones.' The fifth recommends the 
tabulation of facts ' in the order of intensity in which some 
peculiar quality subsists,' — perhaps the most valuable art of 
Discovery. To this precept Herschel very properly appends 
that the value of the device may be frustrated by the interfer- 
ence of counteracting or modifying causes. The sixth rule 
reminds the enquirer ' that such counteracting or modifying 
causes may subsist unperceived,' and urges attention to them 
as a means of explaining exceptions. 

In some general remarks following the enunications of his 
rules, he illustrates the necessity of combining Deduction with 
Induction in complicated enquiries, and explains the nature 
of Empirical Laws, glancing at the fact that they are limited 
in their application to new cases, without stating more pre- 
cisely what their limits are. 

The concluding chapter treats ' of the higher degrees of 
Inductive Generalization, and of the formation and verification 
of theories.' He insists that the assumed agents must be 
verce causa*, f. such as we have good inductive grounds to 
believe do exist in nature.' The value and the test of a hypo- 



WHEWELL'S FACTS AND IDEA8. 095 

thesis he places in its accordance with the facts, and its enabling 
us ' to predict facts before trial.' 

Whewell. The scheme of the late Dr. Whewell's Novum 
Organum Renovation commends itself as strikingly thorough 
and exhaustive. It professes to be * a revision and improve- 
ment of the methods by which Science must rise and grow/ 
founded upon a comprehensive History of Scientific Discovery 
and a History of Scientific Ideas. Now, theoretically, there 
could be no more perfect way of elaborating a body of maxims 
for the aid of the discoverer, than to pass in review, chronolo- 
gically or otherwise, the great physical discoveries that have 
been made, and to study the essentials of the process in each 
case. 

The distinguishing feature of Whe well's scientific writings 
is his persistent driving at an antithesis that he conceives to 
be fundamental, between Ideas or Conceptions and Facts. 
This antithesis is the shaping principle of his system and 
meets us at every point. It regulates the division of his 
history into two parts : the History of Scientific Ideas tracing 
Che gradual development of the so-called ideas, such as Cause 
Affinity, Life, that form the subject-matter of various depart- 
ments of science ; and the History of Scientific Discovery, illus- 
trating how by the instrumentality of Ideas (the highest 
generalities), and of Conceptions (the lower generalities), the 
particular fac's of Nature are united and bound together. 
The same antithesis divides scientific method into two pro- 
cesses. Generalization consisting not in evolving notions from 
a comparison of facts, but in superinducing upon facts con- 
ceptions supplied by the mind. There are two requisites to 
satisfy before this operation can be perfected, namely, that the 
Conceptions be clear and distinct, and that they be * appro- 
priate ' to the Facts, capable of being * applied to them so as 
to produce an exact and universal accordance : ' whence there 
are two scientific processes, the Explication of Conceptions and 
the Colligation of Facts. 

The grand problem of Science is to superinduce Ideas or 
Conceptions upon Facts. The business of the discoverer after 
familiarizing himself with facts, is to compare them with con- 
ception after conception, in the view of finding out after a 
longer or shorter process of trial and rejection, what concep- 
tion is exactly ' appropriate ' to the facts under his consider- 
ation. When the investigator has at length, by a happy gne^. 
hit upon the appropriate conception, he is said to Colligate* 
the facts, to * bind them into a unity.' No distinction is 



696 GROWTH OF THE LOGIC OF INDUCTION. 

drawn in this operation between the generalization of Notions 
and the generalization of Propositions ; the difference between 
them is merged in the one grand purpose of procuring for 
facts clear and appropriate conceptions. 

It is difficult to understand what he supposes to have been 
the origin of the conceptions thus superinduced upon facts. 
He speaks of them as being struck out in the gradual march 
of Science by the discussions and reflections of successive 
thinkers, a view not inconsistent with their derivation from 
the comparison of particulars and the gradual evolution of 
deep and pervading agreements. But he says also that they 
are supplied by tbe mind, while facts are supplied by sense ; 
and the language he holds regarding the suiting of facts with 
their * appropriate ' conceptions, is consistent only with the 
assumption that the mind is a repository of conceptions accu- 
mulated there independently of the experience of particulars. 

By this initial severance of generalities from tht? particulars 
they repose upon, he excluded from his method definitions 
formed by the comparison of facts and the precise statement 
of common features. He rather decries the value of Definition, 
and allows it no place of hononr in his Explication of Conceptions. 
The meaning of a conception is, he thinks, oftener apprehended 
from an axiom than a definition — another instance of his total 
neglect of the distinction between notions and propositions. 

His ' methods employed in the formation of Science/ the 
title of the third Book of the Novum Organon, are three in 
number, Methods of Observation, Methods of obtaining char 
Ideas, and Methods of Induction. As a preliminary to Obser- 
vation, he recognises an Analysis or Decomposition of Facts. 
Under Observation, he discusses chiefly the modes of obtaining 
precise measurement ; he speaks also of the education of the 
senses, but does not attempt to lay down any definite precepts 
farther than recommending the study of Natural History and 
the practice of Experimental manipulation. His Methods of ac- 
quiring clear scientific ideas, are neither more nor less than 
the study of the various departments of science where the 
ideas occur ; the very method that would be recommended by 
a preceptor believing in the evolution of general notions from 
particulars. An aid to the acquisition of clear ideas is Discus- 
sion. 

We find no trace of the three leading Experimental Methods 
in his Methods of Induction, nor indeed of any methods of 
Proof. He conceived that his province was to furnish arts of 
Discovery, in so far as anything was of avail beyond natural 



WHEWELL'S METHODS OF INDUCTION. 

•agacity; and he seems to have thought slightingly of the 
efficacy of the Three Methods as a means to the attainm. 
new laws. His principal arts of Discovery are gi?en a 
the title of * Special Methods of Induction applicable to Q 
tity." The Method of Curves is a device for making appj 
to the eye the result of observations on the concomitant \ 
tion of two phenomena. It * consists in drawing a cur. 
which the observed quantities are the Ordinate, the qoai 
on which the change of these quantities depends be in 
Abcissa' The Method of Meatis is the familiar device of 
eliminating the effects of a constant cause from the conj. 
effects of accidental accompaniments by striking an ; 
several observations. The Method of Least Squares is a s 
what complicated supplement to the Method of Means. When 
more than one mean is proposed, they are each compared with 
the series of actual observations ; the deviations from each 
case in the series are squared, and the mean is affirmed to bo 
most probable, the sum of whose squares is lowest in amount. 
The Metliod of Residues is the method we described under that 
name. 

Under the title of ' Methods of Induction depending on 
Resemblance,' he illustrates the Law of Continuity ( 4 that a 
quantity cannot pass from one amount to another by any 
change of conditions, without passing through all intermediate 
magnitudes according to the intermediate conditions ') ; the 
Method of Gradation, a name given to the process of pn 
that things differ not in kind but in degree) ; and, in tho 
Method of Natural Classification, enforces the importance of 
grouping objects according to their most important resem- 
blances. 

Perhaps the most valuable part of the Organon is the con- 
cluding Book on the Language of Science. Of this subject 
Whewell had made a special study ; his aphorisms on tho 
requisites of philosophical language contain nearly all the 
important points. 

H. — ART OF DISCOVERY. 

It was the distinction of Mr. Mill's handling of Logic to 
draw a clear and broad line between the ^rt and Science of 
Proof and the Art of Discovery. The main business of Logic, 
according to him, is the proving of propositions ; only in an 
incidental way does it aid in suggesting them. 

There is, in the laws of evidence well understood, a power- 
ful indirect incitement to original discovery. A thorough 



698 ART OF DISCOVERY. 

means of testing whatever is propounded for acceptance leads 
to the rejection of the false, and, consequently to a renewed 
search, ending at last in the true. For this reason alone 
would discovery be more rapid in the Mathematical and 
Physical sciences, where verification is easy, than in the 
Mental, Moral, and Political sciences, where the facts are 
wanting in the requisite precision. Kepler was not left in any 
doubts as to whether he had arrived at the true law of the 
periodic times of the planets ; psychologists could not so 
easily satisfy themselves as to the thorough-going concomitance 
of mind and body. 

The Arts and methods of Discovery embrace (1) the Facts, 
that is, Observation ; and (2) the Reasonings on Facts, namely, 
Deduction, Induction, and Definition ; which are all compre- 
hended in the one process, generalization. 

As regards the accumulation of Facts, there is little to bo 
said, and that little is apparent at a glance. Facts are ob- 
tained by active search, enquiry, adventure, exploration. For 
some, we must travel far, and visit many countries ; for others 
we have to lie in wait till occasions arise. For a third class, 
we have to institute experiments, involving contrivance and 
devices, and the creative ingenuity of the practical mind ; all 
which is itself a department of discovery, the least of any 
amenable to rules. 

The arts of Observing were remarked on, in the Introduc- 
tion, as being special for each department, and not a fit sub- 
ject for general logic. The precautions common to all kinds 
of observation, in regard to accuracy and evidence, would be 
worfcby of being recited, provided there could be given a suffi- 
ciency of illustrative instances to make the desired impression. 

From the limitation of the human faculties, the highest 
powers of observation are not usually accompanied w T ith high 
speculative force. Hence, among other consequences, a not 
unusual misdirection of the energies of great observers. 

Passing from the region of fact, we come to the region of 
Generality. A number of individual observations being sup- 
posed, the next thing is to discover agreements among them — 
to strike out identities wherever there are points to be identi- 
fied ; these identities ending either in Notions or in General 
Principles. It may seem a work of vast labour to exhaust 
all the facts of the material and of the mental world ; it is not a 
less labour, although of a different kind, to exhaust all the 
identities among the facts. 

Although the main condition of success, in bringing about 






PSYCHOLOGICAL AIDS TO DISCOVERY. C99 

identities, is a peculiar intellectual aptitude, brio c 0mo 

men in a pre-eminent degree; yet there ai 
and precautions, for increasing the power. S 
aids are suggested by intellectual psychology, otl 
of the methods unfolded in logic. 

The methods growing out of the psychology of the Enid 
tual powers are briefly these :— -to p "mind of a 

store of the related facts ; often to refresh the wool] 
them ; to come into frequent contact with subjects t 
likely to afford comparisons and analogies ; not to stand too 
near any one set of facts so as to be overpowered by I 
specialities; not to be engrossed with the work 
the facts ; and in general, as to matters of great dill" 
keep the mind free from attitudes and pursuits ant 
to the end in view. 

Newton alternately devoted himself to mathematics and to 
the observation and collection of facts in the various subjects 
of natural philosophy; and this alternation doubtle- 
the perfect physical enquirer. 

Frequently an identification has to be embedded in somo 
conception apart from the facts ; as Kepler's laws in ttttmei 
and geometrical statements, the law of sines, <fcc. In such 
cases, proximity to the sources of the conceptions will help to 
bring about the coalition. If mathematical relations, tho 
mathematical knowledge should be kept fresh, and so with 
other subjects. These constructing instances alone trive any 
meaning to Whewell's much iterated antithesis of Fact 
Idea. The identification and generalization of facts often 
happens without any * idea,' any central form, or representa- 
tive beyond the facts themselves ; there is no idea for a circle 
but round things, abstractedly viewed ; and no idea for 
but gravitating bodies compared and regarded in their p 
of agreement. In certain other cases, a concept i 
(not from any intuitive source, but) from some already exi 
generalization, either in the same department, or in an 
department. The 'idea ' for embracing water 
sound vibrations, was found by Newton in the 'Pendulum ;' 
and apart from the facts themselves, no better l idea ' hi 
been given. 

The connexion of Body and Mind has its ' idea ' yet to ( 
There has hitherto prevailed the bad idea of External and In- 
ternal. In short, the most suitable comparison wherein to em- 
brace the relation has notbeen obtained from any source, intuitive 
or other. One approximation is a ' union of distinct sta: 



700, ART OF DISCOVERY. 

The arriving at difficult identifications, that is, the tracing 
of similarities shrouded in diversity, by such devices as have 
been advanced in logic with a more special eye to proof, may 
be viewed in the first place with regard to generalization as 
such ; not distinguishing the notion from the principle or 
proposition. What pertains specially to the induction of the 
general proposition, namely, the concomitance of distinct pro- 
perties, is best considered apart. 

Under the Deductive Method (p. 96) attention was called 
to three helps to the discovery of generalities — multiplication 
of instances, close individual scrutiny of instances, and selec- 
tion of the least complicated instances. A wider view of the 
available resources must now be taken. We have to see how 
far the thorough explication of the reasoning processes, and of 
all the adjuncts to reasoning, called forth by the comprehen- 
sive Logic of Proof, can be brought to bear also in the striking 
ont of suggestions to be submitted to proof or disproof. 

The first great practical lesson derivable from Logic, and 
applicable in a much wider sphere than proof, is to impress us 
with Generality as the central fact of science and of all know- 
ledge transcending individuals. After we have gained posses- 
sion of a certain range of facts, the next great aim is to 
generalize them to the uttermost. This is not all. In pro- 
portion to the compass of any agreement, ought to be the 
pains taken with it, and the prominence given to it. Wo 
have urged, under the Logic of Medicine, the prime import- 
ance of generalizing the Diseased Processes and General Thera- 
peutics, because of the wider compass of their application. In 
everything else, the rule holds. The biologist should take no 
rest until he has exhaustively accumulated instances of the 
great fact of Assimilation, under every possible variation of 
circumstances. In like manner, the physical concomitants of 
mental processes need to be searched out in all their innumer- 
able modes, in order to rise to the generalities of the connexion. 

The severest etiquette of the most punctilious system of 
ranks and dignities in society is as nothing compared with the 
graduation of estimate and of respect to be shown to generali- 
ties of different grades. It is a grave logical misdemeanour 
ever to give an infei'ior generality precedence over a superior, 
or to treat the two as of equal consequence, or even for a 
moment to be unaware of their relative standing. We may 
give all due consideration to the phenomenon of falling bodies 
as a wide fact co-extensive with the surface of the earth ; but 
in presence of the superior sway of the law of gravity through- 



VALUE OF ORDEB AND METHOD. 

out tbe solar system, the terrestrial fact mu .to a 

second place in our esteem. 

The next great application of Method, as nn aid to <! 
consists in the use of the various Forms or Formal 
borated with a view to proof. This is the I 
present subject. 

Logicians have always striven to set forth the value of O 
method, and explicitness, in complicated statements. Hamil- 
ton's dictum— makiug explicit in the statement what ii 
in the thought— has been received as a happv enom 
one function of logic. Mr. Mill remarks,—* One of the g 
uses of a discipline in Formal Lqgic, is to make us aw; 
something that claims to be a single proposition, reallv 
sists of several, which, not being necessarily involved o* 
another, require to be separated, and to be considered each l>y 
itself, before we admit the compound assertion.' This is the 
disentangling or analyzing function of the syllogism, and is 
deservedly extolled as perhaps its highest utility. It 
direct remedy for the weakness of the mind formerly ad\ i 
io(p.39S). 

We may, however, go farther back than the exposition of 
Syllogism for valuable aids growing out of the logical fori 
ties. All the Equivalent Propositional Forms are instrumental 
as means of suggestion. They enlarge the compass of 
given proposition, by unfolding all its implications ; many of 
these not being disposed to rise to view of themsclvc 
without the stimulus of the formal enunciation. Of all tho 
modes of Equivalence, probably the Obverse is the most fruit- 
ful and suggestive ; this has become apparent on many occa- 
sions, in the course of the present work ; wo may inst 
especially negative defining. Next in value is Conner 
converting of A by its legitimate form is a check to tho blunder 
of supposing tho subject and predicate co-extensi?e in uni- 
versal affirmations ; and the arresting of the mind on the 
to impending error seldom ends there, but is also a start in 
the search for truth* Even the immediate inference from tho 
Universal to the Particular is suggestive of facts not pre\ 1 
in the view. 

Much could be said as to the unsystematic but wM. 
mode of Equivalence by Synomyous terms, or by varying 
ways of expressing the same proposition. Although m 
what ensnaring, this is a fruitful and suggestive opera 
Its power consists in resuscitating from the stores of the past 
all the various known examples of the proposition ; to which 



702 ART 0F DISCOVERY. 

also may be added even illustrations and analogies. We know 
from many celebrated instances, how mere opulence of phrase- 
ology gives the semblance, and occasionally the reality, of 
superior insight. The Shakespearian wisdom, the stirring 
apothegms of Pope, have their source, not in the scientific 
process of the intellect, but in the suggestiveness of exuberant 
phraseology. 

The Methods of Inductive Elimination, both directly and 
indirectly assist in Discovery. The collection and comparison 
of instances, to comply with the method of Agreement as a 
method of proof, will in many cases lead to new and improved 
generalizations. A man can scarcely go through the labour 
requisite for establishing a law of high generality upon ade- 
quate evidence, without adding to his knowledge of the law. 
Especially is this likely to happen in working the Method of 
Agreement, whose exigencies are exactly those of inductive 
discovery. 

The same remark applies to the union of Agreement in 
Absence with Agreement in Presence ; and there is the addi- 
tional force and incisiveness that always belongs to the working 
of the negative side. 

The method of Residues, to which Sir John Herschel called 
special attention, was by him expressly commended as an aid 
to Discovery. 

The importance of Concomitant Variations has already been 
signalized, and will be again referred to. 

Without dwelling farther on the specific virtues of the 
several methods, we would call attention to the value of a 
complete scheme of Inductive Proof, in urging a search for 
instances to fill up all its requirements. He that has thoroughly 
mastered the experimental methods, desires to bring up in 
favour of every important principle a series of particulars 
under each one of them separately ; an operation as fertile for 
discovery as it is thorough-going for proof or disproof. 

The remark is not confined to the methods of experimental 
elimination. The greater number of propositions or Jaws may 
derive evidence through the Deductive Method, and through 
Chance and Probability also. The wish to satisfy all possible 
methods of establishing a law is a wholesome stimulus to 
enquire after the very facts that improve the character and 
extend the application of the law. The consilience of Ind ac- 
tion and Deduction is the very highest art that the human 
intellect can command, not merely for proving difficult propo- 
sitions, but for getting hold of propositions to be proved. 



INDUCTIVE ELIMINATION. 703 

All this is to repeat in another shape, and in a pran.hr 
sphere, the function of the Syllogism in insisting thai 
should be produced an explicit major and an i 
premise in any pretended ratiocination. Every nidi 
stance should be viewed in its proper character, bj 
to the method that it subserves. An instance of A 
should be given as such ; a Deductive proof should I 
under that description. If the Logical rules are not B 
but founded on a correct analysis of the scientific | 
the conscious reference to them, on all different < 
must be a relief and a comfort to the perplexed enqnil 

The Deductive operation, understood not formally as in the 
syllogism, but really and materially, as in finding new appli- 
cations and extensions of inductions, is a pure generalizing 
process. It consists in identifying particulars with other 
ticulars, exactly as in the properly inductive operation. It is 
the same march of mind continued and prolonged. An induc- 
tion so called is merely a certain collection of particulars, with 
a generalized expression superadded ; deduction is the bl 
ing in of new particulars. The difference of the two is n 
the mental operation ; it is in the end that is served. The 
inductive particulars are those necessary for giving the gen- 
eralized expression, and for proving it as a law of nature ; the 
subsequent deduced particulars, not being required for 
blishing the generality, receive illumination from the other 
class. In both cases the effort of discovery is identical ; it is 
the bringing together in the mind by the force of resemblance 
a host of particular facts from all times, places, and snbj< 
Before the induction is gained, the particulars contribute to 
its establishment; after it is gained, the new particulars aro 
receivers and not givers of benefit. 

The processes included under Definition — the eaooni f<>r 
Defining, General Naming, and Classification — are proa 
of Discovery directly, and of Proof indirectly. Mr. Mill calls 
them subsidiary to Induction, meaning Inductiv 
Every step indicated under those several heads has an imme- 
diate efficacy either in suggesting generalities, or in purifying 
them from ambiguity, perplexity, and confusion. It 
sible to make a single well concerted move in any of the j 
marked out in these several departments without gaining an 
enlargement of views, or the means of son.o future enlarge- 
ment. 

Everything of the nature of an antidote to inadvertent and 
confused tliinking, everything that reduces information to the 



704: ART OF DISCOVERY. 

shape best suited for recollection and reference, everything 
that facilitates the comparison of resembling facts — must be 
enrolled among the means of Discovery. These various ends 
are explicitly aimed at by the prescriptions contained under 
Definition, Naming, and Classification. To substantiate the 
allegation would be to rehearse the methods explained 
under those heads. The amassing of particulars, positive and 
negative, with a view to Definition, is the express act of gen- 
eralization, and brings with it discoveries of concomitance, as 
well as generalizes notions. All the devices of Naming are 
intended primarily to ease and assist the understanding in 
arriving at new truths. The machinery of Classification is still 
more strikingly the economizing of the faculties in amassing 
and in manipulating knowledge. 

When the generalizing process has expressly in view the 
discovery of laws, or concurring properties, a most material 
help (as formerly seen) is afforded by Tabulation, espe- 
cially according to a scale of degree. Failing this, great stress 
is always laid upon extreme instances. These are the glaring 
and striking instances of Bacon and Herschel (see the Re- 
search on Dew, p. 68). The method of exhibiting gradation 
by Curves is considered one of the best ways of suggesting 
numerical laws. 

Mr. Darwin has given an account of the steps that led him 
to propound the doctrine of Development under Natural 
Selection. It affords an interesting commentary on the fore- 
going enumeration of the causes that prompt original sugges- 
tions. 

' When I visited, during the voyage of H.M.S. Beagle, the 
Galapagos Archipelago, situated in the Pacific Ocean about 
500 miles from the shore of South America, I found myself 
surrounded by peculiar species of birds, reptiles, and plants, 
existing nowhere else in the world. Yet they nearly all bore 
an American stamp. In the song of the mocking- thrush, in 
the harsh cry of the carrion-hawk, in the great candlestick- 
like opuntias, I clearly perceived the neighbourhood of 
America, though the islands were separated by so many miles 
of ocean from the mainland, and differed from it in their 
geological constitution and climate. Still more surprising was 
the fact that most of the inhabitants of each separate island 
in this small archipelago were specifically different, though most 
closely related to each other. The archipelago, with its innu- 
merable craters and bare streams of lava, appeared to be of 
recent origin ; and thus I fancied myself brought near to the 



CONSTRUCTIVE INVENTION. MM 

very act of creation. I often asked myself how these many 
peculiar animals and plants have been produced : the 
answer seemed to be that the inhabitants of the several i* 
had descended from each other, undergoing modification m 
the course of their descent; and that all the ifahal 
the archipelago had descended from those of tiie nearest land, 
namely America, whence colonists would naturally have bee* 
derived. But it long remained to me an inexplicable problem 
how the necessary degree of modification could have 
effected, and it would have thus remained for ever, had I not 
studied domestic productions, and thus acquired a just idea 
of the power of Selection. As soon as I had fully realized this 
idea, 1 saw, on reading Malthus on Population, that Natural 
Selection was the inevitable result of the rapid increase of all 
organic beings ; for I was prepared to appreciate the struggle 
for existence by having long studied the habits of animals. ! 
(Domestication, vol. I., p. 9). 

Throughout the entire logical scheme, the analytic separation 
already insisted on, is an invaluable help to the faculties under 
the complications of natural phenomena. To enable us to view 
separately whatever can be separately viewed is the motive 
for such artificial divisions as Structure and Function in 
biology, Physical Side and Mental Side in psychology, Order 
and Progress, Theory and Practice in politics, Conservation 
and Collocations in cause and effect, Description and Explana- 
tion everywhere. 

The process of Invention in the Arts and business of life, is 
amenable to the general rule of keeping the mind fresh upon 
the most likely sources. The mere cogitating process in prac- 
tical constructions is exactly the same as in the solving of 
geometrical or other problems. Certain data are given, a 
certain construction is required ; there is an intervening chasm 
that has to be bridged. The habit of analytical separation is 
of avail in this instance also. The mind should steadily view 
one point at a time, drawing out connexions with each by 
turns. Thus, to Like a simple geometrical construction : girt* 
the vertical angle, the base, and the al itude of a triangle to 
Construct it. Now the base is given, and we have to lollow 
out the deductions and implications of the two other data — 
altitude and vertical angle — with a view to arrive at some 
known process that will construct the triangle. Le 
sider separately what the altitude will suggest. >'ow, a 
certain fixed altitude implies that the apex ot the triangle will 
lie somewhere in a line parallel to the base ; consequently, if 



706 ART OF DISCOVERY. 

we draw such a parallel, we limit the place of the apex to that 
line. Tarn next to the given angle. Considering how to 
erect npon a given base a triangle with a given vertical angle, 
we are reminded that npon tbe given base may be constructed 
an arc of a circle, such as will contain that angle. The next 
step is to find a means of constructing the proper arc ; the 
operation of discovery is exactly the same ; and brings us at 
length to some construction that we can perform. We then 
unite our two threads hitherto followed out in separation. 
The parallel line first suggested, and the arc next found out f 
give by their intersection an apex to the desired triangle. It 
is our previous knowledge that must forge the links of con- 
nexion between what is given and what is required ; but the 
analytic habit concentrates the attention by turns on each 
datum, and each outgoing from it ; and this is probably the 
utmost that mere art or method can do for us in constructive 
inventions. 

The uncertainty as to where to look, for the next opening in 
discovery, brings the pain of conflict and the debility of 
indecision. This is a case fit to be met by the collective 
wisdom of a generation. There might at intervals be held a 
congress on the condition-of-science question, to decide, accord- 
ing to all the appearances, what problems should be next 
taken up. 

Lessons may be drawn from tbe history of Errors, as well 
as of Truths. All the Fallacies are beacons both in discovery 
and in proof. Every source of confusion is an incubus on in- 
vention. More particularly, the excessive devotion to the con- 
crete, and to the artistic interests nourished by it, may amount 
to a total disqualification for scientific originality, whose very 
existence is in the domain of abstraction. 

Certain widely prevailing tendencies of natural phenomena 
have been indicated as of value in prompting discovery. Such 
are the Law of Continuity, and the maxim that Nature works 
by the Simplest Means. Both these principles are uncertain 
in their scope ; which, however, does not prevent them from 
being used to give suggestions ; it only disqualifies them from 
being conclusive evidence. If we are careful to verify our 
hypotheses, we are at liberty to obtain them from any source. 
Still, the mind that has become largely conversant with the 
ways of nature will find many more fruitful sources of sugges- 
tion than either of those principles. 



RECITAL OF FACTS. 



I. — HISTORICAL EVIDENCE. 






Two leading branches of Evidence, applied in practical life, 
are Legal Evidence and Historical Evidence. The two di 
ments have much in common. The evidence both in courts of 
law and in matters of history is probable, mid approach. 
certainty by the summation of probabilities. 

The following abstract of Historical Evidence represents 
the maxims in use among historians at the present da-. 
summarized by Sir G. C. Lewis. 

The object of History is the recital of facts— of events that 
have actually occurred. 

In the case of contemporary history, the writer may be able 
to rely upon his own observations, or upon original documents 
obtained from authentic sources. Personal knowledge was 
the basis of much of Xenophon's Anabasis, Polybius' History, 
Ccesar's Gaelic War, and Lord Clarendon's History of the 
Kebellion. But the greater part even of contemporary history 
must repose on the evidence of witnesses. 

To a historian, not himself cognizant of the events he nar- 
rates, the sources of information fall under one or other of 
two classes : — (1) Monuments, ruins, coins, and generally all 
ancient remains ; and (2) the evidence of Witnesses. From 
the former exclusively is derived whatever we know of the 
pre-historic age ; in the same way as geology is built on in- 
ferences clrawn from fossils and the nature and position of 
rocks. It is only with regard to history resting upon the tes- 
timony of witnesses that rules of historical evidence apply. 

Two points demand the notice of one seeking to verify any 
alleged historical fact. (1) Does the evidence of the witness 
exist in an authentic shape ? and (2) Is it true ? The first 
regards the accuracy wherewith the evidence has been tr 
mitted to us; the second, the worth of the evidence itself. 
The means of knowledge of the witnesses, the goodflfl 
their memory, their judgment, their general veracity, their 
special interests, — are all to be considered. This the hist 
has in common with a jury or a judge, except that he has io 
deal with men long since dead, and whose character there is 
more or less difficulty in ascertaining. What forms the | 
liar subject-matter of rules of historical evidenee is not t!. 
fore the worth of the evidence, but the aeeuraey u( its u. 
mission. 

The supreme canon of historical evidence is that all te^ti- 



708 HISTORICAL EVIDEKCE. 

mony must be contemporary % or received directly or through 
trustworthy tradition, from contemporaries. ' Whenever any 
event is related in histories written after the time, and not 
avowedly founded on contemporary testimony, the proper 
mode of testing it's historical credibility is to enquire whether 
it can be traced up to a contemporary source. If this cannot 
be done, we must be able to raise a presumption that those 
who transmitted it to ns in writing received it, directly or 
through a trustworthy tradition, from contemporary testi- 
mony. If neither of these conditions can be fulfilled, the 
event must be considered as incurably uncertain, and beyond 
the reach of our actual knowledge/ (Lewis's Methods of 
Politics, I. 270.) 

This rule is universally recognized as inclusive; whatever 
is established by such testimony is credible. There is not, 
however, the same unanimity, in admitting it as exclusive; or that 
whatever is not authenticated by external evidence is uncer- 
tain. A stringent application of the rule makes such havoc of 
ancient history, that many learned men have been tempted to 
exercise their ingenuity in trying to pick out of the mass of 
tradition some certain indications of the true course of events. 
The same impulse that first led to the invention of fabulous 
history — an inability to rest content with a background of 
historical ignorance— now misleads critics and historians. 
They expect by a species of historical divination to strip off 
the false additions to the ancient stories — to sift from the 
fables the grains of genuine fact. Yet it would seem as if the 
utmost that could be gained would be that the event may have 
happened as supposed. To prove that the event did happen, 
nothing can make np for the want of external attestation. 
Internal improbability may enable us to doubt or disbelieve 
an alleged fact ; internal probability cannot assure ns that the 
fact was as alleged ; the only decisive evidence is the testi- 
mony of credible witnesses. 

The difference between the internal and the external stand- 
ards of evidence appears remarkably in the results of their ap- 
plication. Sir G. C. Lewis, refusing to admit internal con- 
sistency or plausibility as a warrant for belief, rejects the 
accepted History of Rome down to the war with Pyrrhus. 
Niebuhr, on the other hand, divides this period into three 
parts that, in his opinion, differ greatly in historical value. 
The era of Romulus and Numa (80 years) he considers wholly 
fabulus; from Tullus Hostilius to the first Secession of the 
Plebs (179 years) is mythico-historical, a twilight of fable 



TRANSMISSION OF WRITTEN EVIDENCE. 709 

and fact; from the Secession of the Plcbs to the w:ir with 
Pyrrhus (213 years) is solid history. It would perhapi be 
too much to condemn Niebuhr's efforts on a j > Midi. 

To what extent a license of guessing may be permitted 
best be seen when it has been tried by different men, II the 
result should be a general concordance of opinion, we might 
reasonably infer that the ancient narratives, although 
conceal, nevertheless betray the truth. If, however, 
method lead to irreconcileable and endless diversity of opinio n, 
it must cease to be regarded as valuable or trustworthy. 

Evidence may be transmitted in two ways, by writing or by 
oral tradition. These may be considered separately. 

The value of a written memorial consists generally in this, 
that its credibility is not impaired by the mere action of time. 
An English mathematician named Craig held that all testi- 
mony was enfeebled by mere lapse of time, and thus the evi- 
dence of Christianity would at length be reduced to zero. 
Assuming that that event would coincide with the end of the 
world, he calculated when the end would come. Laplace 
adopts the same view, and says that even in spite of printing, 
the events that are now most certain, will, in the course of 
ages, become doubtful. But this must be regarded as an error. 
The only deterioration that a document can suffer from mere 
lapse of time is the increased difficulty of weighing the credi- 
bility of the writer. A written memorial has none of the 
disadvantage of a statement handed down orally from one 
person .to another, and losing value at each transmission. 

Yet the evils of transmission are not wholly overcome even 
with written records. Two doubts may arise, (1) whether the 
writing is ascribed to its real author, and (2)whether it is free 
from interpolation and mutilation. 

1 In many cases the original memorial is preserved ; as in 
ancient inscriptions upon stone, brass, or other durable ma- 
terial. Such are the inscriptions, in the arrow-headed cha- 
racter, on the Babylonian bricks, and on other Assyrian 
monuments ; the hieroglyphics engraved on the remains of 
Egyptian architecture; and the numerous Greek a 
inscriptions found in different parts of Asia Minor, Africa, and 
Europe, and belonging to different ages. Ancient coins, with 
their legends, are another original record of the same kind, as 
well as historical sculptures or paintings, such as r [iefil 

on the column of Trajan, or the Bayeux tapestr 
documents, likewise, containing the authentic rec 
important events and public acts, are preserved m the original 



710 HISTORICAL EVIDENCE. 

in national archives. Sach, for instance, is Domesday-book, the 
rolls of Parliament, court records, charters, and other official 
registers and documents kept in public depositories.' (Lewis, 
L201). 

In authenticating books and documents, whose safe-keeping 
is not specially provided for, great difficulty is often experi- 
enced. A mere tradition regarding the origin of a document 
would be exposed to nearly all the doubts that attach to oral 
tradition. ' Hence the importance of archives, chartularies, 
public libraries, and other safe places of deposit, which are 
under the care of trustworthy guardians, appointed and con- 
trolled by public authority.' The law of England requires 
that written documents, before they can be tendered as evid- 
ence, be produced from the proper place of custody. 

The difficulty of ascertaining the genuineness of ancient 
books, is forcibly illustrated by the controversy regarding the 
Platonic Dialogues. Until the close of last century, thirty-six 
dialogues were attributed to Plato on the authority of Thra- 
syllus, whose list dates from about the commencement of the 
Christian era. As, however, Plato died more than three 
hundred years before, the canon of Thrasyllus stands in need 
of corroboration and support. Most of the German Critics 
allow it very little weight, and test each dialogue upon 
own evidence, external or internal, but chiefly internal. This 
unavoidably gives rise to great diversity^ of opinion, and there 
is little agreement as to what ought to be rejected or retained. 
Ast, the least sparing critic, leaves only fourteen out of thirty- 
six. Mr. Grote, on the other hand, discards the German 
criticism, and putting little stress upon the indications of 
authorship contained in any reputed dialogue of Plato, searches 
for more decisive evidence, so far as it can be got k in the 
history of the books mentioned by Thrasyllus. 

Plato died B.C. 347, and left his works to the care of the school 
continued under Xenophanes and Speusippus. We do not 
possess any list of their master's works resting on their autho- 
rity, and the first solid ground we reach (apart from the few 
incidentally mentioned or alluded to by Aristotle) is an extract 
from the works of the Grammaticus Ai'istophanes, who lived 
at Alexandria from B.C. 260 to B.C. 184. * He comes thus a 
century after Plato, and nearly two centuries before Thra- 
syllus. He divided the dialogues into trilogies, and several 
of these are mentioned by Diogenes Laertius. They are re- 
markable as containing the names of some of t£e compositions 
that are least acceptable to the critics, and that would be hard 



EXAMPLE OF PLATO'S DIALOCill glj 

to vindicate on internal evidence. These are tares, Kpii 
Minos, Epistolae, Sophistes, Politicus. It would be ink 
ing to know what means Aristophanes had of difltingai 
the genuine from the spurious works, if anv puch istei 

For two centuries after the death of Plato, the A 
was kept up as a philosophical school, with an unbn 
cession of presidents. The chief treasure ot the school 
the works of the master. It cannot be too much to assume 
that there was provided a safe custody for the MSS. of I 
and a ready means of verifying any alleged works. i\. ; 
better off in this respect than any of his great contemporaries, 
Socrates, Demosthenes, Euripides, or Aristophanes. 

Aristophanes, the Grammaticus, was head of the Alexan- 
drian Library. He was taught by Callimachus, who preceded 
him in the office of Chief Librarian. Callimachus is the author 
of the * Museum/ a general description of the Alexandrian 
Library ; and less important authors than Plato, as e.g. Denio- 
critus, are mentioned by him. It is then highly probable that 
such a library as that of Alexandria would contain copies of 
one of the foremost Greek philosophers. And, considering 
the ease of verification, it is most likely that the Librarian 
would assure himself that his copies were authentic. 

There were, in the time of Thrasyllus, spurious dialogues. 
Whence came these, and by what criterion did he discard 
them ? If Aristophanes and Thrasyllus (who appears also to 
have been connected with Alexandria) depended upon the lib- 
rary there, they must be allowed to speak with great weight ; 
but if they proceeded wholly or partially upon internal evidence, 
they have less claims on onr attention than the better-equipped 
modern critics. Mr. Grote supposes that the spurious works 
were made for the demand in Greece and Asia Minor, and 
for the library started by the Kings of Pergainus as a rival to 
the Alexandrian. 

So much for the difficulty of settling the real author 
The other point to be determined is the freedom of existing 
copies from spurious additions or omissions, accidental or 
intentional. 

In the first place, errors will accidentally creep in, by the 
mere act of copying. It is impossible to guarantee strict 
accuracy in transcription. This is recognised in jurisprudence, 
and the English law refuses to admit any copy where the 
original can be produced. But the reason of the law doc 
apply with the same force in history. A very slight alte: 
in a deed might sometimes alter the meaning of it ; and, no 
31 



712 HISTORICAL EVIDENCE. 

over, there is often an exceedingly powerful temptation to 
tamper with deeds. Now, the value of a copy of MS. 
depends on its accuracy, and the motives for falsifying history 
are far weaker. It is therefore considered that the works of 
classical authors are preserved to us substantially as they were 
when published. Such variations as there are do not affect 
the general accuracy of the copies that have reached us. 

In the second place, changes may be made intentionally, to 
6uit a purpose. We are told that Solon inserted a verse in 
the Iliad with a view to confirm the title of the Athenians to 
the possession of Salamis. At an early period, authentic lists 
or canons of authors and their works were prepared to guard 
against deception. Short writings are most easily forged, and 
hence there are numberless forgeries of letters ; but we find 
examples of falsification at greater length in the poems of 
Ossian. Ecclesiastical writings contain many forgeries, made for 
the purpose of propagating or confirming opinion. The motive 
for executing forgeries is often to make money by arousing 
curiosity ; but in such cases as Ossian, it is merely the pleasure 
of deceiving the world. Literary forgeries are generally 
detected by internal evidence — by inconsistencies, anachron- 
isms, imitations of subsequent writers, and other marks of 
recent composition. 

When we have sufficient assurance that a work is both 
authentic and genuine, written by its reputed author, and not 
tampered with in the course of transmission, we have still to 
consider the worth of the testimony. Besides examining our 
author's means of information — whether he writes as an eye- 
witness or at second hand, or at what other remove from eye- 
witnesses — we must enquire into his character for veracity and 
his motives to depart from the truth. 

There is often intentional perversion or suppression of the 
truth, especially in Autobiography, as Caesar's Gallic Wars, 
and Napoleon's Memoirs of his Campaigns. Vanity, a love of 
the marvellous, and party spirit, operate in the same direction. 
There are Catholic and Protestant histories of the Reforma- 
tion ; Whig and Tory histories of England. The accounts of 
modern campaigns and military operations differ very much 
according to the side the writer belongs to. Many inaccuracies 
arise from not taking the trouble to investigate the truth. 
History may be blended with fiction for a didactic or moral 
purpose, as in Xenophon's Cyropaedia. 

The ancient historians departed from strict truth, by intro- 
ducing into their works speeches composed by themselves. 



MYTHICAL HISTORY. 

One fourth of the history of Thucvdides is composed of such 
speeches. Lucian thought it a suihcient excuse for introduc- 
ing fictitious speeches, that they were suitable to the charac- 
ter of the speaker, and appropriate to the subject. Pol , 
is the only writer of antiquity who condemns the pri 
he says, the object of the historian is not to astonish the re 
but to record what was actually done or said. This opinion 
has been followed by modern historians, and the manufacture 
of speeches has therefore ceased. The same thing, how 
in substance, is still done, although introduced as part of the 
history, namely, interpreting acts and suggesting motives. 
It is a great, though perhaps not uncommon, error, to treat as 
history what thus owes its origin to conjecture. 

Another perversion of history is mythical history. 'The 
original author of such a legend must, no doubt, be at first 
conscious that it is the spontaneous product of his own inven- 
tion, unattested by any external evidence. But the fiction is 
suggested by prevailing ideas and feelings; it intenve 
existing facts and customs into its texture ; it furnishes an 
apparent support to institutions or practices for which the 
popular mind seeks an explanation ; it fills a void which is 
sensibly felt, and supplies food for an appetite whose demands 
are at once urgent and general. The inventor of such a legend, 
therefore, differs altogether from the author of a novel or 
romance, who lays before the public a tale avowedly fictitious, 
and which they accept as such.' Examples may be found in 
Greek mythology, in the fabulous heroes of mediaeval chivalry, 
and in the lives of mediaeval saints. Such legends have a use, 
not as describing events, but as throwing a reflected light on the 
circumstances and character of those who invented, believed,and 
circulated them. The most difficult case to the historian 
is not pure mythology, but the blending of myth and history, 
which lures men on to search for fact, but leaves them un- 
able to distinguish it from fiction. The history of Greece, 
from the first Olympiad to the Persian war, and of Rome, 
from Tullus Hostilius to the Punic wars, illustrates this inter- 
mediate period of twilight and uncertainty. 

The second mode of transmitting evidence — Oral Tradition, 
loses credit very rapidly with the lapse of time. An account 
of an event, diminishing in evidentiary value at each remove 
from the original eye-witness, very soon ceases to have any 
value at all. This has always been more or less recogn: 
Polybins confined himself to what he learned from i 
witnesses of the preceding generation, and thus begins his 



714 HISTORICAL EVIDENCE. 

consecutive history about twenty years before his birth. 
Newton thought that oral tradition might be trusted for 80 
or 100 years ; and Voluey remarks that the Red Indians had 
no accurate tradition of facts a century old. 

The average value of oral tradition may be enhanced in 
various ways. During the pauic caused by the mutilation of 
the Mercuries, and the fear of treasonable attempts to esta- 
blish a despotism, the Athenians recurred to the government 
of Pisistratus and his sons, which had begun nearly 150 years 
and ended 100 years before that time. Thucydides describes 
the Athenians as referring, entirely by oral tradition, to the 
attempt by Cylon — a fact at the time 180 years old. That 
event had however created a hereditary curse in the powerful 
family of the Alcmaeonidae, and the memory of it was revived 
at different times by public acts. The Dies Alliensis, the 
anniversary of the fatal battle of the Allia, was doubtless kept 
up by uninterrupted usage from B.C. 390. Festivals, emblems, 
antiquated offices, serve to fix tradition, and keep alive the 
recollection of events. The Inter r ex ^ in Rome, who continued to 
be appointed during the Republic in the vacancy of the consul- 
ship, was a reminiscence of a period of elective kings. The 
King of the Sacrifices, like the King Archon at Athens, is also 
a decided indication of the regal period. There were, more- 
over, many buildings, monuments, and public places in Rome 
associated with the names of kings. The existence of laws, 
like the Twelve Tables, inscribed on metal or stone, may serve 
to perpetuate a correct oral tradition. 

Rubin o, the author of a work on the early Roman Constitu- 
tion, has laid down some rules on this subject. He divides 
oral tradition into two classes, one referring to the constitution, 
and the religious and civil institutions connected with it, the 
other embracing the more common material of history, wars, 
negotiations, and the striking events that give interest to the 
history of Rome. This last alone was committed to the ex- 
clusive keeping of oral tradition, and was much more liable 
to error and uncertainty than the traditions relating to the 
constitution. To some extent, constitutional usage implies a 
knowledge of precedents. Such information in all probability 
existed at the beginning of the Second - Punic war ; but it 
might not reach far back without the help of documents. 
There is no reason to suppose that accurate knowledge would 
have gone back beyond a century. It is not possible to draw 
any broad line between constitutional history,' and the common 
events of history ; we could not discuss the changes in the 



ARGUMENT.— CATEGOREMATIC.— DICTUM. 

English Constitution during the seventeenth century, without 
a knowledge of the events that gave birth to tluni/ 

There is one case where oral transmission makes an appr 
to the value of transmission by writing. This happens whm 
the memory is assisted and checked by vm of words, 

especially if the form be metrical. Ca?sar tells us that the 
secrets of the Druidieal religion were contained in a great 
number of verses, in committing which to memory a druid 
would spend twenty years of his life. In like manner, tho 
Iliad and Odyssey were perpetuated by a race of professional 
reciters and rhaj)sodists. 



K. — EXPLANATION OF SOME LOGICAL TERMS. 

The following terms, not being deemed essential to any of 
the important doctrines of Logic, may not have been made 
fully understood in the previous exposition. As they occa 
ally occur in logical discussions, short explanations of them 
are here appended. 

Argument is used in severa 1 . different senses. Apnrt from 
its more popular significations, a disputation, a chain of rea- 
soning, and even a chain of events (the argument of a play), 
its meaning is not fixed and uniform among logicians. iSome 
apply it to an entire syllogism, premises and conclusion, some 
to the premises only as the grounds of the conclusion, while 
Hamilton maintains that its proper meaning is the middle 
notion in a reasoning, — ' what is assumed toargae sometli 
So Mansel holds that the word should be applied only to 
the Middle Term. 

Categorematic. — A distinction is drawn between words that 
can stand alone as subject or predicate of a proposition, as 
man, stone (Categorematic) ; and words that can stand only 
in company with other words, as all, none (£tyttcategorematic). 

Dictum de own et HULLO. — This applies directly to the 1 
Figure alone. It is usual to give similar principles for the 
other Figures, and among these we may notice the cZ/c/agiveu 
by Mr. Mansel in his notes on Aldrich (p. 80). 

4 Principle of second figure. Dictum de l)iv>rso. If a cer- 
tain attribute can be predicated (affirmatively or negatively) 
of every member of a class, any subject of which it cannot be 
so predicated, does not belong to the class. 

' Principles of third figure. I. Dictum de exemplo. If a 
certain attribute can be affirmed of any portion of the members 



716 EXPLANATION ON SOME LOGICAL TEKMa 

of a class, it is not incompatible with the distinctive attributes 
of that class. II. Dictum de excepto. If a certain attribute 
can be denied of any portion of the members of a class, it is 
not inseparable from the distinctive attributes of that class/ 

Enthymeme. — A syllogism with one of its premises sup- 
pressed in the enunciation. Hamilton argues against the 
prominence given to Enthymeme as a division of syllogisms, 
on the ground that they are not a special form of reasoning, 
but only an elliptical mode of expression. He also shows 
(what is done more elaborately by Mr. Mansel) that Aristotle 
understood by Enthymeme not an elliptical syllogism, but 
4 a syllogism from signs and likelihoods/ or a syllogism with 
the major premise only probable. 

Ignava Ratio or Sophisma pigrum is the master fallacy of 
Fatalism. It might be classed with fallacies of Non-observa- 
tion. The Fatalist argues that, if a thing must happen, it 
will happen whether he interfere or no ; overlooking that his 
own agency is one of the co-operating causes. 

Intuitive — Symbolical. — We often employ words and sym- 
bols without fully realizing their meaning. This Leibnitz 
called Symbolical as distinguished from Intuitive, Knowledge, 
ideas and sensations fully realized in consciousness. We can 
conceive a yard, a mile, or even ten or twenty miles, in 
the full reality of the extent ; but of the distance between the 
earth and the moon, the sun, or one of the fixed stars, we have 
no proper conception ; we may, however, express such dis- 
tances in figures, which are intelligible as such. This would 
be a symbolical conception. 

Modals. — (See Part I., p. 99). The opposition of Pro- 
positions has been applied to Modals, in the following state- 
ments. 

If the matter be necessary, all affirmatives must be true, and 
all negatives false, 

If the matter be impossible, all negatives must be true, and 
all affirmatives must be false. 

If the matter be contingent, all particulars must be true, and 
all universals false. 

Here the meaning of c necessary ' is no more than univer- 
sally true, as all men are mortal, all matter gravitates. ' Im- 
possible ? is universally false ; all men are gods. * Contin- 
gent' means partly true and partly false; Some men are wise. 

Porphyry's Tree. — This is a tabular arrangement showing 
different grades of generality. The example chosen ranges 
from the summum genus Substance, to the infima species Man, 



PKOrHYRY's TREE. 7] 7 

ending with two individuals. It may bo exhibited thus, in a 
form better described by the Greek name, Porphyry's J 
(*\t>f) :— 

Subs tan co 
Corporeal Incorporeal 

(Body) 
Animate Inanimate 
(Living Body) 
Sensitive Insensitive 

(Animal) 
Rational Irrational 
(Man) 
Socrates Plato 

^redesignate is a term applied by Hamilton to propositions, 
having their quantity expressed by one of the signs of quan- 
tity, All, None, &c. The contrasting term is hremdesignaU* 
The terms commonly used in logic are Definite, Indefinite. 

Simple Apprehension is defined by Whately as 4 the opera- 
tion of the mind by which we mentally perceive or form a 
notion of any object.' It is the same as Perception, whereby 
we know things in the actual or concrete — a house, a tree. 
By another faculty, designated Abstraction, we conceive things 
in the general. 

Sufficient Reason. — Under this title Leibnitz stated the 
law of Causality, Everything that exists must have a * suffi- 
cient reason ' for its existence. The attempt has been made to 
prove certain truths, such as the law of perseverance of uni- 
form motion in a straight line, on the ground that no suffi- 
cient reason can be given why a body should either lose its 
velocity or deviate to one side or the other. The same line of 
remark has been used with the principle of virtual velocities. 

Sophisma Polyzeteseos and Sophisma Heterozeteseos are 
two ingenious Greek Sophisms. The first was alluded to 
nnder Definition. Choosing a word having a doubtful margin 
of application, the sophist asks whether it applies to sucli and 
snch a case, and goes on putting the question to one contiguous 
case after another, until he has drawn the respondent palpably 
beyond the range of the word, when he demands the difference 
between the last case admitted and the first refused. Such 
words as heap, calf, &c, are suitable : the sophist asks— Was 
it a calf to-day, will it be a calf to-morrow, next day, and bo 
on ; the respondent cannot say on what day it ceases to be a 
calf, and becomes a heifer. The Heterozeteseos (Sophism of 



718 EXPLANATION ON SOME LOGICAL TERMS. 

Irrelevant Question) decoys a person into committing himself 
by a categorical answer — 'Have you cast your horns? — If 
you answer, I have ; it is rejoined, Then you have had horns : 
if you answer, I have not, it is rejoined, Then you have them 
stilL 1 



INDEX. 



Abstraction, allied to Analysis, 683. 
Abstract Ideas, dispute regarding, 5. 
Abstract name, completion of gener- 
alizing process, 52. 
value and abuse of, 53. 
Accidens, 76. 
Accidentis, fallacia, 674. 
Activity, a source of fallacies, 607. 
Adjectives, connotative, being gener- 
alized names, 49. 
JEquivocatio, 673. 
A dicto secundum quid ad dictum 

simpliciter, 602, 624, 675. 
^Esthetic emotions, a source of fal- 
lacy, 613. 
A dicto simpliciler ad dictum secitn- 

dum quid, 674. 
Affinity, chemical, defined, 473. 
maximum of, 417. 
in Mineralogy, 524. 
in Botany, 532. 
in Zoology, 540. 
in diseases, 596. 
A fortiori, 164. 

Agreement, intellectual property of, 
3. 
the basis of Reasoning, 8. 
basis of Definition, 385. 
defines the limits of Explanation, 

351. 
stated in classification, 422. 
in the arrangement of chemical 

elements, 476. 
statement of, in Mineralogy, 529. 
in Botany, 535. 
in Zoology, 543. 
in diseases, 596. 
Method of, 279. 

fundamental maxim of, 278. 
in Biology, 500. 



Agreement, Method of, in Politics, 
565. 
in Medicine, 590. 
frustrated by plurality of causes, 

308. 
protected against plurality of 
causes, 309. 
an aid to Discovery, 702. 
in Absence, basis of, 279. 
Universal, the sole evidence for 

Inductive truths, 237. 
the test of uniform co-existence, 

244. 
proof of concomitant properties 

in Natural kinds, 245. 
the sole Inductive Method, 277. 
fundamental mode of Proof, 344. 
Algebra, notions of, 432. 
account of, 443. 
highest operation of, 445. 
Algebraic Geometry, notions of, 402. 

account of, 448. 
All, two meanings distinguished by 

De Morgan, 187. 
Ambiguity of terms, 602, 616. 
Amphibolia, 673. 
Analysis, Chemical, 627. 
Logical, 628. 

allied to Abstraction, 39, 629. 
applied to Induction, 684. 
Grammatical, 684. 
Critical, 684. 
Mathematical, 685. 
preliminary to elimination, 272. 
in Psychology, 511. 
in Society, 570. 
conformed to rules of division, 

427. 
an aid to Discovery, 705. 
Analytic judgment, 76. 



720 



INDEX. 



Analogy, as a form of Inference, 
373. 
does not amount to Proof, 373. 
examples of, 375. 
Analogies, false, 372, 624. 
Analogical Hypotheses, 377. 
Animals and Plants contrasted, 495. 
Antecedence, invariable, not causa- 
tion, 268. 
causal usually complicated, 271. 
Apprehension, simple, 717. 
Approximate Generalizations, 365. 
probability of, stated in numbers, 

366. 
how brought nearer certainty, 368. 
open to sophistry, 369. 
A priori, applied to knowledge, 10. 
Argument, 715. 

Aristotelian contrasted with Bacon- 
ian logic, 642. 
Arithmetic, definitions of, 433. 
. ultimate notions of, 434. 
account of, 442. 
proof in, 443. 
Associations, a source of fallacy, 

615. 
Astronomy, its place among the 

Sciences, 630, 636. 
Averages, 321. 

Axiom of Syllogism, various forms 
discussed, 155. 
proof of, in experience, 159. 
Hamilton's forms, 160. 
as given by Thompson, 161. 
as given by De Morgan, 162. 
not derivable from the " Laws of 
Thought," 162. 
Axioms, nature of, 224. 
requisites of, 224. 
only two Mathematical, 224. 
of Inductive origin, 225. 

Bacon, contributions to inductive 

methods, 6S7. 
Belief, the nature of, 12. 

inherently excessive, 607. 

law of, explains intense convic- 
tions, 225. 
Biology, scope of, 488. 

divisions of, 492. 

notions of, 494. 

propositions of, 496. 



Biology, conservation of Force in, 
498. 

Empirical laws in, 498. 

logical methods of, 500. 

Hypotheses of, 502. 

as basis of Medicine, 577. 
Body, substance of, 660. 
Body and Mind, 357, 376, 505. 
Botany, arrangement of characters 
in, 531. 

maximum of affinity in, 532. 

grades in, 534. 

agreement and difference in, 535. 

peculiarity in exhibition of differ, 
ences, 536. 

index in, 538. 

Calculus, notions of, 432. 

account of, 448. 
Canons of Syllogism, 149. 

according to Hamilton, 151. 

special for each Figure, 152. 
Canons, special, derived from Axiom, 

163. 
Categorematic, 715. 
Categories, of Aristotle, 661. 
Categorical Imperative, meaningless, 

376. 
Causation, law of, 20, 226. 

uniformities of, as a branch of 
Logic, 239. 

law of, expressed, 245. 

obverse denied, 246. 

three aspects of, 247. 

practically viewed, 247. 

scientific, 249. 

fallacy of, 250. 

as Conservation of Force, 251. 

as an instrument of elimination, 
276. 

unfolded in three maxims of elimi- 
nation, 277. 

induction of, 343. 

rests on Agreement alone, 345. 

as an Empirical law, 345. 

discriminated from Co-existence, 
381. 

not distinguished from Co-exist- 
ence, 688. 

propositions of, in Biology, 497. 

in Politics, 55$, 564. 

contradiction of, incredible, 379. 



INDEX. 



721 



Cause, an alleged intuition, 11. 
to be sought among the antece- 
dent circumstances, 267. 
not proved by invariable antece- 
dence, 268. 
the unconditional invariable ante- 
cedent, 268. 
material, formal, efficient, final, 
248. 
Causes, composition of, 268. 
combination of, 327. 
real, 359. 
Chance, computation of, a resource 
under Intermixture of Effects, 
313. 
coincidence explained, 315. 
principle of computation, 316. 
applicable where other methods 

fail, 316. 
combined with law, 319. 
submerging a small uniformity, 

319. 
in Biology, 501. 
in Psychology, 516. 
in Medicine, 592. 

elimination of, an aid to Discov- 
ery, 702. 
Character, Science of, based en Psy- 
chology, 516. 
elements of, 518. 
as affected by Conservation, 518. 
influences on, 519. 
not classified like Natural History, 

520. 
peculiarities of, 521. 
human, in Politics, 556. 
Characters, descriptive, sequence of, 
414. 

in Chemistry, 478. 
in Mineralogy, 523. 
in Botany, 531. 
in Zoology, 538. 
Chemical force, conservation of, 355. 
combination, not a union of forces, 

370. 
defined by contrast, 393. 
Chemistry, fundamental fact of, 472. 
propositions of, 473. 
arrangement and methods of, 474. 
elements of, classified, 474. 
descriptive method of, 478. 
agreement and difference in, 483. 



Chemistry, empirical laws in, 481. 
law of Conservation in, 484. 
hypotheses in, 485. 
nomenclature of, 486. 
notation of, 487. 
Class, two meanings of, definite and 

indefinite, 280. 
Classification, golden rule of, 383, 
415. 
Methods of, 414. 
descriptive characters in, 414. 
grades of, 418. 
terminates with Species, 420. 
statement of agreements and dif- 
ferences in, 422. 
Index, 424. 
of Characters, 520. 
Sciences of, 522. 
an aid to Discovery, 704. 
Co-existence one of the three Uni- 
versal Predicates, 103. 
as Order in Place, 103. 
as Co-inherence of Attributes, 

104. 
uniformities of, as a branch of 

Logic, 239, 243. 
induction of, 241. 
proof of, by Universal Agreement, 

244. 
propositions of, in Biology, 296. 

in polities, 556. 
and Succession, common to sub- 
ject and object experience, 
656. 
Collective names, singular or gener 

al, 48. 
Colligation of Facts, 695. 
Collocation of Circumstances, 251. 
degrees of complexity, 260. 
elliptically spoken of as the Cause. 

262. 
as Potential Energy, 2f,4. 
the effect of expended force, 2 
in Politics, 564. 
Colony, example of positive defini- 
tion, 388. 
Colour, not intrinsically objective, 

657. 
Complex Propositions, how far mat- 
ter of Logic, 85. 
Complications of Cause and Effect* 
271. 



722 



INDEX. 



Compositionis et Divisionis, fallacia, 

674. 
Comprehension, 50. 
practically more important than 

extension, 333. 
Hamilton's syllogism in, criticized, 
180. 
Conceptualism, 6. 
Concept, formation of, 383. 
Conception, formal, 473. 
Concomitance, discovery of laws of, 
419. 
in Zoology, 539. 
Concomitant, a predicable, 76. 
separable and inseparable, 77. 
Variations, 292. 

fundamental maxims of, 278. 
interrupted by critical points, 

294. 
as a means of suggestion, 294. 
tables of, for Discovery, 295, 
under intermixture of effects, 

403. 
in Biology, 500. 
in Politics, 567. 
in Medicine, 591. 
Concrete names, 54. 
Conditional Propositions, 85. 

Syllogism, involves no inference, 
117. 
Confusion, fallacies of, 602, 616. 
Consciousness, 507. 
testimony of, 665. 
Connotation, of General Names, 49. 
Conservation of Force, law stated, 
251. 
proved by universal agreement, 

237. 
explained, 250, 252. 
evidence of, 344. 

has same proof as Causation, 266. 
not an a priori conception, 267. 
in Chemistry, 484. 
in Biology, 498. 
in Medicine, 589. 
under re-distribution, 460. 
in Character, 518. 
Consistency, Principle of, 14, 108, 

645, 670. 
Contiguity, extension of names 

through, 403. 
Continuity, law of, empirical, 338. 



Continuity, a help to Discovery, 697, 

706. 
Continuous Comparison, 295. 
Contradiction, principle of, 16. 
Contradictory, propositions, 93. 

misapplication of the name, 94. 
Contraries, expression of, made pre- 
cise by De Morgan, 56. 
basis of De Morgan's additions to 
syllogism, 184. 
Contrary propositions, 92. 
Contrast, in defining, 385. 
animals with plants, 495. 
exhibition of, in Chemistry, 483. 
Conversion, Simple, 113. 
Fallacies of, 114. 
by Limitation, per accident, 114. 
obverted, or by Negation, or Con- 
traposition, 116. 
Copula, 44. 

meanings of, 182. 
Correlative names, 55. 
Correlation of Forces, see Conserva- 
tion. 
Credibility, consistency with proved 

inductions, 379. 
Crystallization, an example of Agree- 
ment, 284. 
explanation of, confirmed by Joint 
Method, 291. 
Curves, method of, 697, 704. 

Deduction, first principles of, 17. 
explained, 40. 
why placed before Induction and 

Definition, 41. 
laws of, 645. 

as general presumption, 284. 
involves observation of facts, 

325. 
two stages of complexity, 327. 
simple, extension of a law, 327. 
combination of causes, 329. 
fallacies of, 625. 
Deductive Method, three requisites 
of, 325. 
in Psychology, 513. 
in Politics, 567. 
in Medicine, 592. 
alone, insufficient in Politics, 
572. 
Sciences, how constituted, 216. 



INDEX. 






Definition, as verbal predication, 71. 
exhaustive and unexhaustive, 71, 

72. 
explained, 38, 384. 
fundamentals of, 385. 
Positive Method of, 386. 
margin of transition, 390. 
Negative Method of, 392. 
deductive, 395. 
the language of, 395. 
by synonyms, 396. 
per gemes et differentiam, 74, 396. 
by Analysis, 396. 
notions not susceptible of, 398. 
mixed with Real predication, 582, 

587. 
fallacies of, 626. 
neglected by Whewell, 696. 
an aid to Discovery, 706. 
De Morgan, divisions of Terms, 51. 
on Positive and Negative names, 

56. 
enumeration of Propositions, 90. 
additions to syllogism, 182. 
Demonstration, based on Induction, 

219. 
Denotation, of General Names, 49. 
Derivative laws, 334. 

various kinds of, 334. 
limited application of, 336. 
of wider application than Em- 
pirical, 342. 
in Politics, 568. 
Description, of chemical bodies, 478. 
not to be mixed with explanation, 
483, 584. 
Descriptive terminology, 407. 

characters, sequence of, 414. 
Development hypothesis, 502. 
Dew, research on, an example of 

elimination, 298. 
Dictum de omni et Nullo, 1 55. 
Difference, Method of, fundamental 
maxims of, 278. 
explained, 287. 
where indecisive, 289. 
in Politics, 566. 
in Medicine, 591. 
exhibition of, in Chemistry, 483. 
Differences, statement of, in Classi- 
fication, 422, 529. 
in Botany, 535. 



Differences, statement of, difficult in 
Botany, B 
in Zoolo. 
in Diseases, 5 'J 6. 
Differentia, 73. 

Dignity, a source of fallacies, 613. 
Dilemma, 121. 
Discovery, Art of, 697. 

distinguished from Proof by Mill, 

697. 
three aids to, 326. 
secondary in Logic, 327. 
Disease, definition of, 575. 
Disjunctive Propositions, 85. 
Disjunctive Syllogism, involves no 

inference, 119. 
Division, an aspect of classification, 
425. 
rules of, 426. 
a mode of grades, 427. 
fails with undefined classes, 428. 
Documents, invalidated by two 
doubts, 709. 

Efficient Cause, 248. 
Electricity, Conservation of Force in, 
257. 
characters and branches of, 468. 
Elimination, of Cause and Effect, 
271. 
weapons of, 276. 
is Proof, 279. 
of chance, 314. 
Empirical laws, explained, 333. 
various kinds of, 334. 
criteria of, 335. 
limited application of, 336. 
established by Universal Agree- 
ment, 237. 
more precarious than derivative, 

342. 
in Chemistry, 484. 
in Biology, 498. 
in Psychology, 514. 
in Politics, 568. 
Enthymeme, 716. 
Equality, uniformities of, as a branch 

of Logic, 239. 
Equality and inequality, one of the 
three Universal Predicates, 
103. 
Equivalence of propositions, 107. 



724 



INDEX. 



Equivalent terms, as an aid to Dis- 
covery, 702. 
Essential attributes, 74. 

predication, in Psychology, 509. 
Excluded Middle, principle of, 17. 
Exclusion, Bacon's process of, 688. 
Existence, has no real opposite, 69. 
propositions of elliptical, 107. 
means Object and Subject indis- 
criminately, 620. 
Experience, the source of knowl- 
edge, 9. 
the proof of the Axiom of the Syl- 
logism, 159, 226. 
the proof of Causation, 226. 
Experiment, advantages of, 273. 
in Biology, 500. 
in Politics, 563. 
Experimental Methods, apply only to 
Cause and Effect, 240. 
deductive, in character, 277, 

345. 
explained, 279. 
examples of, 297. 
frustration of, 306, 312, 313. 
in Psychology, 512. 
in Politics, 565, 572. 
in Medicine, 590. 
how far anticipated by Bacon, 

687, 689. 
given by Herschel, 694. 
neglected by vYhewell, 696. 
Experimentum cruris, 365. 
Explanation of Nature, a joint effect, 
347. 
intermediate links, 348. 
subsumption of laws, 349. 
limits of, 351. 
fallacious, 354. 
Extension, 50. 

fundamental property of the Ob- 
ject, 657. 
Evidence, assertions beyond reach 
of, incredible, 382. 
i Historical, 423. 

supreme canon of, 707. 
internal and external, 708. 
two modes of external, 709. 
transmitted by writing, 709. 
transmitted orally, 713. 

Facts and Ideas, 695, 699. 



Fallacies, Aristotelian and Scholastic, 
673. 
Whately's division, 676. 
Mill's classification of, 599. 
a priori, 599. 
of observation, 600. 
of generalization, 601. 
of ratiocination, 601. 
of confusion, 602, 616. 
position of, 603. 
extralogical, 605. 
tendencies to, 606. 
logical, 624. 
knowledge of, aids Discovery, 

707. 
in Politics, 572. 
Fear, a source of fallacy, 612. 
Feeling, two-sided, 2. 
Feelings, a source of fallacy, 609. 
Fever, definition of, 581. 
Figures, 136. 

relative value of, 146. 
reasons for different, 146. 
Figures diciionis, faliacia, 674. 
Final Cause, 248. 

Food, an example of positive defini- 
tion, 388. 
Force, definition of, 251. 
chief predicates of, 251. 
Conservation of, 21. 
Form and Matter, 639. 
Formal Logic, too narrow, 645. 
Cause, 248. 

thinking explained, 640. 
requires inductive verification, 
648. 
Freedom of the will, 344, 621. 
Functions of living bodies, 491. 

Function and Structure viewed 
separately, 493. 

General Name, explained, 48. 
Generality, Names classed according 
to, 47. 

higher and lower, 54. 

degrees cf, in Notions, 64. 

fixed grades of, in Botany, and in 
Zoology, 65. 

degrees of, in Propositions, 78. 

of Proposition follows Notion, 78. 

as classifying Propositions, 78. 

as a basis of Definition, 385. 



INDEX. 



72o 



Generalization, identical with Expla- 
nation, 446. 

the highest ambition of Science, 
456. 

approximate, 465. 

fallacies of, 601. 

excessive tendency to, 608. 

as an art of Discovery, 279, 698. 
Genua and species, movable names, 
except in Natural History, 65. 

a predicable, 73. 
Geometry, notions of, 432. 

definitions of, 434. 

ultimate notions of, 436. 

axioms of, 438. 

postulates of, 439. 

order of topics in, 446. 

proof of Euclid's fourth proposi- 
tion in, 447. 
Glaring instances, 690, 704. 
Government, forms of, 549, 553. 

definition of, 551. 

functions of, 552. 

local and central, 554. 

defines Public and Private, 554. 
Grades of generality, great import- 
ance of, 700. 

in classification, 418. 

Statement of, suited to discovery 
of concomitance, 419. 

in Mineralogy, 528. 

in Botany, 534. 

in Zoology, 542. 

in Diseases, 596. 
Gravity, an example of Hypothesis, 
460. 

contraction of, incredible, 379. 

Hamilton, additions to syllogism, 
178. 
Quantification of Predicate, 178. 
syllogism in Comprehension criti- 
cized, 180. 
Health-Disease, indefinable, 264. 
Heat, generated by collision, 253. 
conservation of, 254. 
unprofitable dissipation of, 255. 
definition of, 467. 
heads of the science of, 467. 
propositions of, 470. 
structural, should be stated in 
chemical formulae, 487. 



Herschcl, contributions to Induc- 
tion, 693. 
History, Philosophy of, 5 48. 

basis of Politics, 561. 

perversions of, 712. 
Hotnonymia y 505. 
Hypothesis, various meanings of, 358. 

of known agencies desirable, 159. 

of a new agent permissible, 361. 

as a representative fiction, 362. 

differs from geometrical abstrac- 
tions, 364. 

analogical, 377. 

in Chemistry, 485. 

in Biology, 502. 

in Psychology, 515. 

in Politics, 569. 

in Medicine, 593. 
Hypothetical Inference, 1 1 6. 

Idea and Facts, 695, 699. 
Identification of a Minor, when dif- 
ficult, 218. 
not an induction, 235, 328. 
Identity, principle of, 16. 
Idola, Bacon's, 609. 
Ignava Ratio, 717. 
Ignoratio etenchi, 602, 623, 675. 
Immediate Inference, 107. 

by Added Determinants, 109. 
fallacies of, 625. 
Import of Propositions, 100. 
Hobbes's view, 100. 
not the reference of something 
to a class, 101. 
Inconceivability of the opposite, ex- 
plained, 223. 
rejected as ultimate test of truth, 
665. 
Incredibility, inconsistency with 

proved inductions, 379. 
Index, to a classification, 424. 
in Mineralogy, 530. 
in Botany, 538. 
in Zoology, 544. 
in Diseases, 597. 
Individual, our idea of, a conflux 
of generalities, 7. 
Induction, first principles of, 19. 
explained, 40, 231. 
would furnish Formal processes, 
650. 



726 



INDEX. 



Induction, a branch of Logic, 651. 

improperly so called, 233, 235. 

cannot be brought under the syl- 
logism, 233. 

a prerequisite of deduction, 325. 

in difference of subject, 3*71. 

postulate of, 502. 

fallacies of, 625. 

growth of, 68*7. 
Inductive, Discovery, 326. 

Methods an aid to Discovery, 702. 

Syllogism, 233. 
Infimae species, 63. 
Inflammation, definition of, 583. 
Intermixture of Effects, 310. 
in Politics, 565. 
in Medicine, 591. 
International law, 548. 
Intuition, an alleged source of knowl- 
edge, 10. 
Intuitive — symbolical, 716. 
Invention, how assisted, 705. 

Joint Method of Agreement and 
Difference, 291. 
counteractive to plurality of 

causes, 310. 
in Politics, 566. 
in Medicine, 591. 
an aid to Discovery, 703. 
Judgment, formal, 641. 

as a synonym for proposition, 

80. 
its significance with Aristotle, 80. 
Jurisprudence, 548. 

Knowledge, the act of, includes al- 
ways two things, 3. 

conjoins Agreement and Differ- 
ence, 4. 

of two kinds, called Object and 
Subject, 5. 

Individual or Concrete, and Gen- 
eral or Abstract, 5, 22. 

origin of, in Experience, 9. 

limited by our sensibilities, 13. 

nature and classification of, 21. 

should be true, 22. 

conveyed in propositions, 44. 

relativity of, appears in language, 
54. 
Kinds, 63. 



Kinds, exemplifv co-inhering attri 
butes, 241. 

Language, truths expressed in, 42. 

fallacies of, 616. 
Law, confused meanings of, 643, 617. 
metaphorical use in " Laws of Na- 
ture," 239. 
involved in Government, 552. 
combined with Chance, 319. 
Laws of Nature, by preeminence, 

239. 
Liberty, 550. 
Life, definition of, 488. 
Light, undulatory theory of, 361. 
commutation of, not established, 

258. 
production of, an example of 

Agreement, 286. 
definition and subsidiary notions 
of, 468. 
Likeness and Unlikeness, common 
to subject and object expe- 
rience, 655. 
Love, a source of fallacy, 612. 

Margin, doubtful, in definition, 390. 
Mathematics, Logic of, 429. 

the best example of a Deductive 
Science, 429, 647. 

notions of, 430. 

propositions of, 432. 

definitions of, 433. 

axioms of, 437. 

leading branches of, 442. 
Materia Medica, 581. 
Method, expresses part of the func- 
tion of Logic, 35. 

an aid to Discovery, 701. 
Mind, substance of, 660. 

definition of, 505. 

difficult to estimate quantity in, 
517. 
Mind and Body, 357, 376, 505. 
Mineralogy, scope of, 522. 

relations to Chemistry, 522. 

arrangement of characters in, 52S. 

maximum of affinity in, 524. 

grades in, 528. 

agreement and difference in, 529. 

index for, 530. 
Material Cause, 248. 



INDEX. 



727 



Material, names of, singular, 48. 
Matter, as Resistance, 657. 

defined by positive method, 391. 
by negative method, 393. 

constitution of, a hypothesis, 363. 

Force, Inertia the same fact, 455. 

physical properties of, 464. 
Mechanics, 462. 
Medicine, scope of, 575. 

based on Biology, 577. 

definitions of diseases in, 581 

general diseases in, 579, 581. 

specific diseases in, 586. 

propositions of, 588. 

experimental methods in, 590. 

elimination of chance in, 592. 

the deductive method in, 592. 

hypotheses in, 593. 

classification in, 695. 
Miner, identification of, not an in- 
duction, 235. 
Mnemonics, 147. 
Modals, 99, 717. 

Molar forces, conservation of, 252. 
Molecular attractions, 464. 
Molecular forces, enumerated, 254. 
Motion, laws of, reduced to one, 

458. 
Monarchy, example of positive defini- 
tion, 387. 
Moods, 138. 

usual enumerations justified, 153. 
Muscular Irritability and Putrefac- 
tion, an induction, 303. 
Mystery, 356. 

Names, why considered at beginning 
of Logic, 45. 

defined, 46. 

denote things, not ideas of things, 
46. 

variously classified, 47. 

De Morgan's divisions of, 51. 

go in couples, 54. 

meaning of, increases with oppo- 
site, 60. 

loosely extended, 402. 

transitive application of, 403. 

class, 409. 

of generalities should be short, 
410. 

new, 410. 



Names, precautions in appropriating 
old, 4 12. 
expressive, 414. 
different, held to imply difl. 

things, 418. 
improper use of, 420. 
Naming, general, value of, 401. 
first requisite of, 402. 
second requisite of, 407. 
Nature, explanation of, 346. 

ambiguity of the word, 616. 
Negation, variously expressed, 58. 
Negative names, 55. 
singular or plural, 57. 
of a real property, also real, 58. 
Necessary Truth, 14. 
Necessity, meanings of — certainty, 
220. 
implication, 221. 
inconceivability of the oppo- 
site, 223. 
Nerve force, conservation of, 258. 
Newton, contributions to Induction, 

693. 
Nomenclature, 412, 414. 

of Chemistry, 486. 
Non causa pro causa, 675. 
Non sequitur, 675. 
North-east wind, an example of 

Agreement, 283. 
Nota notoz est nota rci ipsius, 156. 
Notation, of Chemistry, 487. 
Notion and Proposition, not distin 

guished by Whewell, 696. 
Notions, contrasted with Proposi- 
tions, 61. 
disguised as Propositions, 6.6. 
of singular or plural constitution, 

63. 
indefinable, ultimate, 398. 

Object, analysis of, 486. 

attributes special to, 657. 
Object-Subject, highest real couple, 
59. 

greatest of all antitheses, 653. 

attributes common to, 655. 
Observation, why not a department 
of Logic, 36. 

the basis of Induction, 234. 

compared with Experiment, 278. 

in Biology, 500. 



728 



INDEX 



Observation, in Politics, 561. 

erroneous, causes of, 562. 

fallacies of, 600. 

as an art of Discovery, 698. 
Opposition, of propositions, 92. 

error in cgmraon square, 94. 

amended square, 97. 

Aristotle's square, 98. 
Obversion, formal, 109. 

material, 111. 
Order, valuable aid to Discovery, 701. 
Order and Progress, 555, 570. 
Oxygen, exemplary description of, 
479. 

Parity of Reasoning, 235. 
Pathology, general, 579. 
Per genus et differ entiam, 385, 396. 
Persistence of Force, see Conserva- 
tion. 
Petitio Principn, 602, 623, 675. 
Physics, Molar, divisions of, abstract 
and concrete, 452. 
notions of, 452. 
propositions of, 454. 
definitions of, 455. 
axioms of (laws of motion), 458. 
concatenation and method of, 
462. 
Physics, Molecular, departments of, 
463. 
notions of, 464. 
propositions of, 469. 
predominant methods of, 472. 
Plants and Animals contrasted, 495. 
Plato's dialogues, how authenticated, 

710. 
Plurality of Causes, 246. 

how far subject to uniformity, 246. 
bearing of, on the Experimental 

Methods, 307. 
in. Politics, 565. 
in Medicine, 591. 
Plurium Inter rogationum, 676. 
Political Economy, 548. 
PoUtics, two divisions of, 547. 
embraces several sciences, 549. 
province of, 549. 
Descriptive, 550. 
Theoretical, defined, 556. 
propositions of, 558. 
universal propositions of, 559. 



Politics, Theoretical, limited proposi- 
tions of, 560. 
methods of, 561. 
experiment in, 563. 
causation in, 564. 
method of agreement in, 565. 
other experimental methods in, 

566. 
deductive method in, 567. 
hypotheses in, 569. 
simplifying of, 570. 
fallacious methods in, 572. 
Practical, End in, 573. 

based on Theoretical Politics, 

574. 
origin of political devices in, 
575. 
Porphyry's tree, 716. 
Positive names, 55. 
Post hoc ergo propter Ao<?, 675. 
Postulate, the universal, 664. 
Potential energy, 259. 

an aspect of Collocation, 264. 
Practice, logic of, 545. 

maxims of, in Politics, 575. 
Predesignate, 717. 
Predicables, 73. 
Predication, verbal, 76. 
confounded with real, 68. 
in plural notions, 69. 
in Natural Kinds, 69. 
verbal not tautological, 70. 
final analysis of, 660. 
Predicates, three universal, 102. 

Mr. Mill's scheme of, 106. 
Premises, 135. 

Prerogative Instances of Bacon, 688. 
Presentative and Representative, 7, 

640. 
Primary qualities of matter, 657. 
Probable Inference, explained, 365. 
may be estimated, 366. 
how made more precise, 368. 
Probability, 320. 
explained, 321. 
principle of, 321. 
rules of, 322-. 

applied to Causation, 324. 
an approximate generalization, 

366. 
comparison of, 381. 
in Biology, 501. 



INDEX. 






Probability, in Psychology, 516. 

ambiguity of the word, 618. 
Progress and Order, 555, 570. 
Proof or Evidence, the scope of Logic, 

34, 279. 
Proposition, a, contains two names, 
and two notions, 274, 292. 

verbal, 67. 
Propositions, 73. 
Proprium, 74. 

exemplified in Mathematics, 432. 
Psychology, scope of, 505. 

subordinate notions of, 507. 

propositions of, 509. 

logical methods of, 511. 

empirical and derivative laws in, 
614. 

hypotheses in, 515. 

chance and probability in, 516. 

suggesting arts of Discovery, 699. 

a Concrete Science ? 636. 

Quality, of Propositions, Affirma- 
tive or Negative, 83. 
an ineradicable distinction, 83. 
designations of, 84. 
Quantification of Predicate, 86. 
makes two propositions in one, 

88. 
additions to syllogism, basis of, 
178. 
Quantity, of Propositions, Total or 
Partial, 81. 
Universal and Particular, inapt 

names, 82. 
Indefinite, 82. 
one of the three universal Predi- 
cates, 333. 
common to Object and Subject ex- 
perience, 655. 
subject-matter of Mathematics, 

429. 
designations of, 81. 
sciences of, Deductive, 103. 
uniformities of, as a branch of 
Logic, 239. 

Ratiocination, fallacies of, 601. 
Realism, 5. 

fallacy of, 619. 
Reasoning, used in defining Logic, 
30. 



Reasoning, founded on Similarity, 8 
from particulars to particular! 

tot. 

chain of, reducible to a series of 

syllogisms, 215. 
causes of; complicated, 119, 
formal, 641. 
Reduclio ad impo&tibdt, 141. 
Reduction, 147. 
Relativity, law of, 2. 

Names classed according to. r 

universal, 61. 

as affecting Notions, 

as classifying Proposition 

as a basis of Definition, II 

basis of an enumeration of things, 

485. 
fallacies of, 621. 

of Proposition follows Notion, 79. 
Relative terms, for special relation- 
ships, 60. 
names, 55. 
Representative Fictions, 362. 

in Medicine, 594. 
Residues, Method of, 279, 295. 
in Politics, 569. 
an aid to Discovery, 702. 
Resistance, 657. 

Sanguine Temperament, a source 

of fallacy, 611. 
Science, the perfect form of Knowl- 
edge, 23. 
characteristics of, 23. 
problem of, as conceived by 
^'hewell, 6'.*6. 
Sciences, classified, 25. 
Abstract and Concrete, 25. 
Abstract, 25. 
Concrete, 28. 
Practical, 2^. 

defined, 545. 
Classification of, Bacon, 627. 
D'Alembert, »: 
Encyclopedia Metropolitans, 

628. 
Xeill Amott, I 
Comte, 629. 
Herbert Spencer, I 
criticism of Spencer's scheme, 
634. 



730 



INDEX. 



Secondary qualities of matter, 657. 

Laws, importance of, 332. 
Self-interest, a source of fallacy, 620. 
Series, Classification by, 295. 
Serial order, in classification, 417. 
Similarity, law of, 3. 

the foundation of Reasoning, 8, 

370. 
basis of scientific explanation, 346. 
extension of names through, 402, 
405. 
Singular Name explained, 48. 

Propositions, syllogism of, 159. 
Smelling, due to oxidation, induc- 
tively proved, 297. 
Society, notion of, 547. 

structure of, 550. 
Solid defined by positive method, 
390. 
by negative method, 393. 
Sophi&ma Heterozeleseos, 717. 
Pigrum, 715. 
Polyzeteseos, 716. 
Sorites, or heap, 390, 717. 
Space, an abstraction, 11. 

characterized, 657. 
Species, a predicable, 73. 
Species, importance of in classifica- 
tion, 420. 
infima, 421. 
in Mineralogy, 528. 
in Botany, 535. 
in Zoology, 542. 
Statistics, Political, 549, 562. 

Medical, 592. 
Structure of Living Bodies, 490. 
and Function viewed separately, 
463. 
Subject, explained, 655. 

attributes special to, 659. 
Subject-Object, highest real couple, 
59. 
greatest of all antithesis, 653. 
attributes, common to, 655. 
Substance, a supposed intuition, 11. 

fundamental attribute, 660. 
Succession, one of the three Uni- 
versal Predicates, 105. 
as Order in Time, 105. 
as Cause and Effect, the chief 
part of Induction, 106. 
Sufficient Reason, 600, 717. 



Sumption and Subsumption, 146. 
Syllogism, defined, 133. 

examples of, 165. 

additions to, by Hamilton, 178. 
by De Morgan, 182. 
by Boole, 190. 

Numerically Definite, 188. 

functions and value of, 207. 

how far a material process, 211. 

axiom of, reposes on experience 
226. 

an aid to Discovery, 703. 

of the Will, meaningless, 376. 
Sympathy, a source of fallacies, 610. 
Symbolical— Intuitive, 716. 
Symbols, of Propositions, 86. 
Synonymous Propositions, 123. 
Synonyms, definition by, 396. 

as an aid to Discovery, 701. 
Synthesis, Chemical, 681. 

Logical, 683. 

does not apply to Simple Deduc- 
tion. 684. 

Grammatical, 684. 

Mathematical, 685. 
Synthetic judgment, 76. 

Tabulation, as an Index Classifica- 
tion, 530, 597. 
as an aid to Discovery, 704. 
Tabular arrangement, Bacon's, 687. 
Terminology, descriptive, 407. 
Terms, of syllogism, 364. 
Therapeutics, general, 580. 
Things, enumeration of, 652. 

Mr. Mill's enumeration of, 661. 
Thought, Laws of, 16, 641. 
definition of Logic, 30. 
too limited to make a Universal 
Postulate, 664. 
Time, an abstraction, 240. 
Tradition, oral, value of, 713. 

approaching to written evidence, 
715. 
Truths, known immediately, 32. 
known by the mediation of other 
truths, 82. 

Ultimate Laws op Nature, limited 

in number, 353. 
Uniformity of Nature* supposed in 
Deduction, 19. 



INDEX. 






Uniformity of Xature, enters into 
Theoretical Logic, 645. 
the ultimate major premise of all 

Induction, 671. 
a plurality not a unity, 238. 
axiom of, fundamental, 227. 
Uniformities among effects of same 
cause, 335. 
limited in application, 341, 342. 
of remote causal connection, 334. 
Universe, of a term, 56. 

Vanity, a source of fallacies, 603. 
Variation of circumstances, 273. 
Verification, 330. 



Verification, in Politl 
Veres Cauue, 35U. 

Wjiewell, contributions to Ii 

tion, 6'J5. 
Wonder, a source of fallacy, CI 2. 



Zoology, difficulties of, 538. 
arrangement of 

538. 

laws of Concomitance in, 
maximum of affinity in, D 
grades in, 542. 

agreement and difference in, 543, 
index in, 544. 



in, 



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ST. AUGUSTINE 
FLA. 









32084 







